NATIONAL INSTITUTE OF SCIENCE EDUCATION AND RESEARCH

BHUBANESWAR

SCHOOL OF PHYSICAL SCIENCES

COURSE NAME: FIRST YEAR (SECOND SEMESTER) PHYSICS LABORATORY

COURSE CODE: P-142 COURSE CREDITS: 2

LIST OF EXPERIMENTS

1. Conversion of Voltmeter to Ammeter and vice-versa.

2. Study of Electromagnetic Damping.

3. Determination of the Horizontal Component of Earth’s magnetic field using

a tangent coil galvanometer.

4. Magnetic field variation along the axis of a circular coil and a Helmholtz

coil.

5. Determination of the resolving power of telescope.

6. Determination of Dispersive power of the material of the prism using

spectrometer.

7. Study of Newton’s rings.

8. Laser diffraction and interference.

9. Study of Polarization and verification of Malus’s law.

Conversion of voltmeter to ammeter and vice-versa

Objective

• Convert a given voltmeter to an ammeter of suitable range and calibrate theammeter so prepared.

• Convert a given (micro or milli) ammeter to a voltmeter of suitable range andcalibrate the ammeter so prepared.

Apparatus

Voltmeter, (micro or milli) Ammeter, resistance boxes (1Ω – 10kΩ and fractional),wires, digital voltmeter and milli-ammeter or multimeter, power supply (0–5 volt).

Working Theory

Voltmeter measures voltage drop across resistance by putting it in parallel tothe resistance as shown in Fig 1. The internal resistance of a voltmeter is quitehigh (Rm ≫ R) and, therefore, when connected in parallel the current through thevoltmeter is quite small (iv ≈ 0). This keeps the current ir flowing through theresistance R almost the same as when the voltmeter was not connected. Hence, thevoltage drop (ir R) measured across the resistance by a voltmeter is also almost thesame as the voltage drop without the voltmeter across the resistance.

On the other hand, ammeter measures current through resistance by connecting itin series with the resistance, Fig 1. An ammeter has very low resistance (Rm ≪ R) andchanges the effective resistance of the circuit only by a tiny amount (R + Rm ≈ R),not altering the original current by too much. Therefore, the current measured bythe ammeter is about the same as without the ammeter in the circuit.

V

iv

Rir

Rm

A

Ri

Rm

Fig 1. Schematic diagram of voltmeter and ammeter connections

Conversion of voltmeter to ammeter

Since the internal resistance of a voltmeter is much greater than ammeter, forconversion to ammeter we need to decrease the voltmeter’s internal resistance byadding appropriate shunt i.e. resistance in parallel to the meter. Let the range of thevoltmeter be 0 – V0 volt and we convert it to an ammeter of range 0 – I0 Amp.

To calculate the shunt resistance, we need to know the resistance of the voltmeter.This is done by half-deflection (potential divider) method using the circuit shown in

1

Fig 2(a). Let Rm be the internal resistance of the voltmeter, and when R = 0 thevoltmeter reading is Vm, the current through the circuit is i = Vm/Rm. But whenR 6= 0 and the voltmeter reads Vm/2, the current in the circuit reduces by halfimplying i/2 = Vm/(R + Rm). The voltmeter resistance Rm is given by,

Vm

2Rm

=Vm

R + Rm

⇒ Rm = R (1)

Once Rm is determined, the shunt Rsh can be determined by noting that, to getfull-scale reading V0 of the voltmeter we need a maximum current of Im = V0/Rm.For full-scale reading of voltmeter V0 corresponding to full-scale reading I0 of ourconstructed ammeter, we need to send a current Im through the voltmeter and theremaining Ish through the shunt. Therefore the shunt resistance Rsh, the maximumresistance that can allow minimum Ish current, is calculated as,

Ish = I0 − Im =⇒ Rsh =V0

Ish

(2)

E

V

Ri/2

Rm

A

E

V

Im

RshIsh

RI0

Rm

converted

ammeter

Fig 2. (a) Circuit for determination of voltmeter resistance, (b) circuit for using thevoltmeter as ammeter.

Conversion of ammeter to voltmeter

Converting an ammeter to a voltmeter involves increasing the resistance of theammeter. This is done by adding a high resistance in series with the ammeter. Letthe range of the ammeter be 0 – I0 Amp and we convert it to a voltmeter of range 0– V0 volt.

To calculate the series resistance Rss, we first determine the ammeter resistanceusing the circuit Fig 3(a). Let Rm be the internal resistance of the ammeter, thenthe current flowing through the circuit is i = E/(R + Rm), where E is the inputvoltage. The voltage drop across R is Vr and the current is ir = Vr/R. Since i = ir,the ammeter resistance Rm is obtained as,

Rm =(E − Vr) R

Vr

(3)

2

To calculate Rss we note that the voltage drop across the ammeter, showing fullscale reading I0, is Vm = I0 × Rm. To make ammeter full-scale to read full-scalevoltage V0, the remaining voltage Vss = V0 − Vm should drop across Rss and fromthis consideration we calculate series resistance as,

Vss

Rss

=Vm

Rm

=⇒ Rss = Rm

Vss

Vm

(4)

E

A

RRm

Vr

E

R

V

A

Rss

Rm Vss

converted

voltmeter

Fig 3. (a) Circuit for determination of ammeter resistance, (b) circuit for using theammeter as voltmeter.

Experimental procedure

1. The first step to convert a voltmeter to an ammeter is to determine the resistanceRm of the voltmeter. Make the circuit connections as shown in Fig 2(a).

2. Keeping R = 0, adjust the supply voltage E so that the voltmeter shows largereadings Vm.

3. Choose suitable R to reduce the voltage recorded in voltmeter to half, Vm/2.The voltmeter resistance is then Rm = R. You may choose to plot the Rm

against serial numbers and draw an average line through them to obtain theaverage Rm.

4. Calculate the shunt resistance Rsh and fabricate the circuit shown in Fig 2(b).Use a digital ammeter or a multimeter, set to appropriate range, as the standardammeter.

5. Changing the supply voltage for a fixed R (chosen such that the maximumcurrent in the circuit is little above I0), record the converted and the standardammeter readings Inew and Istandard.

6. Plot the calibration curve Inew - Istandard versus Istandard.

3

7. Begin converting an ammeter to a voltmeter by determining the resistance Rm

of the ammeter. Make the circuit connections as shown in Fig 3(a). Theresistance R in series with the ammeter must be kept at large value to preventlarge current from flowing through the ammeter and damaging it.

8. Change R appropriately and each time measure the voltage drop across it Vr

with a digital voltmeter or a multimeter. Also change the supply voltage Eto change the Vr. Calculate Rm from these set of readings either by directaveraging or by ploting Rm versus serial number and drawing an average line.

9. Calculate the series resistance Rss and fabricate the circuit as shown in Fig3(b). Use a digital voltmeter or a multimeter, set to appropriate range, as thestandard voltmeter.

10. Changing the supply voltage for a fixed R (chosen such that the maximumvoltage in the circuit is little above V0), record the converted and the standardvoltmeter readings Vnew and Vstandard.

11. Plot the calibration curve Vnew - Vstandard versus Vstandard.

Data recording and Observations

Converting voltmeter . . . . . . volt to ammeter . . . . . . Amp

Full-scale reading of the voltmeter = . . . . . . voltNumber of divisions in the scale = . . . . . .Value of minimum division of the voltmeter = . . . . . . volt

Full-scale reading of the converted ammeter = . . . . . . AmpNumber of divisions in the scale = . . . . . .Value of minimum division of the converted ammeter = . . . . . . Amp

Table 1. Measurement of voltmeter resistance Rm

Serial Full deflection Half deflection Rm AverageNo. Vm volt R Ohm Vm/2 volt R Ohm Ohm Rm Ohm. . . . . . . . . 0 . . . . . . . . . . . . . . . . . .. . . . . . . . . 0 . . . . . . . . . . . . . . . . . .. . . . . . . . . 0 . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . 0 . . . . . . . . . . . . . . . . . .. . . . . . . . . 0 . . . . . . . . . . . . . . . . . .

Calculation of Rsh:Im = V0/Rm = . . . . . . AmpIsh = I0 − Im = . . . . . . AmpRsh = V0/Ish = . . . . . . Ohm

4

Table 2. Calibration of the converted Ammeter

Converted ammeter Standard ammeter CorrectionInew Amp Istandard Amp Inew − Istandard Amp

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

Converting Ammeter . . . . . . Amp to Voltmeter . . . . . . volt

Full-scale reading of the ammeter = . . . . . . AmpNumber of divisions in the scale = . . . . . .Value of minimum division of the ammeter = . . . . . . Amp

Full-scale reading of the converted voltmeter = . . . . . . voltNumber of divisions in the scale = . . . . . .Value of minimum division of the converted voltmeter = . . . . . . volt

Table 3. Measurement of ammeter resistance Rm

Serial E R Vr Rm = (E − Vr)R/Vr AverageNo. volt Ohm volt Ohm Rm Ohm. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .

Calculation of Rss:Vm = I0 × Rm = . . . . . . voltVss = V0 − Vm = . . . . . . voltRss = RmVss/Vm = . . . . . . Ohm

Table 2. Calibration of the converted Voltmeter

Converted voltmeter Standard voltmeter CorrectionVnew volt Vstandard volt Vnew − Vstandard volt

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

5

2. ELECTROMAGNETIC DAMPING OF A COMPOUND PENDULUM

Objective: To study the Electromagnetic damping of a compound pendulum.

Introduction:

Damping plays an important role in controlling the motion of an object. It is an effect, which

tends to reduce the velocity of a moving object. A number of damping techniques are used in

various moving, oscillating and rotating systems. These techniques include, conventional friction

damping, air friction damping, fluid friction damping and electromagnetic (eddy current)

damping. Electromagnetic damping is one of the most interesting damping techniques, which

uses electromagnetically induced currents to slow down the motion of a moving object without

any physical contact with the moving object.

To understand the phenomenon of electromagnetic damping, we need to know about

electromagnetic induction (discovered by Michael Faraday in 1831) and eddy currents (also

known as Foucault currents - discovered by Leon Foucault in 1851). Electromagnetic induction

is a phenomenon, in which an electromotive force (emf) is induced in a conductor, when it

experiences a changing magnetic field. An emf is induced when either the conductor moves

across a steady magnetic field or when the conductor is placed in a changing magnetic field. Due

to this induced emf and the conducting path available, induced currents (flow of electrons) are

set up in the body of the conductor. These induced currents are in the form of ‘eddy currents’

which are electrons swirling within the body of the conductor like water swirling in a whirlpool

(eddy).

The eddy currents swirl in such a way as to create a magnetic field opposing the change in the

magnetic field experienced by the conductor in accordance with Lenz’s law. Thus the eddy

currents swirl in a plane perpendicular to the magnetic field. These eddy currents interact with

the magnetic field to produce a force, which opposes the motion of the moving conductor or

object. The damping force increases as the distance of the conductor decreases from the magnet.

This damping force is also

strength of the magnetic field and the induced

eddy currents and hence the velocity of the object.

Thus faster the object moves the stronger is the

damping force. This means that as the object

slows down, the damping force is reduced,

resulting in a smooth stopping motion.

In this experiment, a magnet is attached to a

compound pendulum and a metal sheet is placed

at certain distance from the magnet. The metal

sheet should be placed in such a way that it is

parallel to the plane of oscillation and

perpendicular to the length of the magnet as

shown in Figure 1. While the

will change and induce eddy current in the metal plate.

Apparatus

Compound pendulum with a pointer

plate with holder, mirror, graph paper

watch.

Theory

Consider a compound pendulum

axis through P and is displaced from its equilibrium position by an angle

θ (see Fig. 2). In the equilibrium

body is vertically below P. The distance GP is

m and I is the moment of inertia of the body through the axis P

equation of motion of for small amplitude

θ&&

Thus the solution of Eq. 1 becomes,

also proportional to the

strength of the magnetic field and the induced

eddy currents and hence the velocity of the object.

Thus faster the object moves the stronger is the

ans that as the object

slows down, the damping force is reduced,

ng in a smooth stopping motion.

magnet is attached to a

and a metal sheet is placed

distance from the magnet. The metal

sheet should be placed in such a way that it is

parallel to the plane of oscillation and

perpendicular to the length of the magnet as

While the pendulum oscillates, the magnetic flux passing through the metal

will change and induce eddy current in the metal plate.

with a pointer, tripod stand, set of magnets, copper

graph paper to mark position of pointer, stop-

Consider a compound pendulum pivoted about a horizontal frictionless

axis through P and is displaced from its equilibrium position by an angle

. In the equilibrium position the center of gravity G of the

body is vertically below P. The distance GP is L, the mass of the body is

is the moment of inertia of the body through the axis P. Then the

for small amplitude oscillation is given by

… … (1)

Thus the solution of Eq. 1 becomes,

Fig. 1: Experimental set up

Magnet

Mirror

pendulum oscillates, the magnetic flux passing through the metal Fig. 1: Experimental set up

Compound pendulum

Copper plate

Fig. 2: Compound Pendulum

l

( )tsinθθ 00 ω= … …. (2)

where 0θ is the maximum angular amplitude, 0ω = 2π/ T0 = I

mgL. So time period for free

oscillation of the pendulum is given by

mgLI

2πT0 = … … (3)

When the oscillation is damped due to any resistance in the path such as friction or eddy current

etc, the damping force exerted at the free end of the rod is directly proportional to velocity, v, of

the free end. Let γ be the constant of proportionality called as damping coefficient, then this

force can be written as

F= -γv = - γlω … … (4)

where l= actual length of the rod, ω= angular velocity and the negative sign indicates that the

force is always directed opposite to the velocity. Then torque is given by

•

−=−= θF 22 lll γωγ … … (5)

Thus the equation of motion for a damped oscillation is given by

θmgLθθI 2 &&& lγ−−= … … (6)

The solution of this modified equation is

= … … (7)

where 2

2Iτ

lγ= , is called as decay constant and is the angular frequency of damped oscillation.

Thus, θ becomes maximum (but < θ0 due to exponential decay function in Eq. 7), for = 2,

where n= 0, 1, 2… If T1is time period of this damped oscillator, then it attains maximum

displacement at times, t=nT1. Hence the maximum displacement of the pendulum decreases

exponentially with time as given by the following equation:

= … … (8)

Equation 8 can be rewritten in terms of an equation of a straight line as follows:

ln θmaxθ0≈ ln xn

x0= -

τ n … … (9)

where x0 is the initial and xn is the final linear amplitude after n oscillations. Knowing τ from the

slope of the straight line, the damping co-efficient can be calculated as

γ= 2 I

… … (10)

Procedure

1. The compound pendulum is mounted on a tripod stand with two pin pivot arrangement.

Make sure that the pendulum does not slip from the pivot.

2. Fix the magnet to the pendulum using adhesive tapes.

3. Place a mirror vertically very close to the pin attached to the pendulum as a pointer.

Adjust the position so that the image of the tip of the pin can be seen in the mirror

avoiding parallax error. A graph sheet is pasted on the mirror to mark and note the linear

amplitudes of the pendulum. Mark the equilibrium position on the graph sheet.

4. Place the copper plate at a distance, say about 15 mm, so that the plane of copper plate is

perpendicular to the axis of the magnets (see Fig.1).

5. Measure the time period for 10 oscillations by using a stop watch provided. Repeat it for

3 to 5 times to find the average time period of oscillation.

6. Displace the pendulum from the mean position to a position of initial amplitude, x0 (say

about 20mm), and then leave it to oscillate. Note the final amplitude after 2 oscillations.

Repeat it for at least three times, and then find the average value of x2.

7. Repeat the above step for 4, 6, 8, 10 oscillations keeping the initial position fixed.

8. Fill up the observation table and plot a graph between the number of oscillations, n vs

ln x0

. Determine the slope using straight line fitting and find decay time τ.

9. Finally, calculate the damping co-efficient ‘γ’ using the given values of I and l.

Observations

Given: Moment of inertia of the supplied rod, I = 0.0235 kgm2

Length of the rod, l = 0.61m

Table 1: Time period of damped oscillation

d = ……

Sl.

No.

Time for 10

Oscillations (sec)

Time period T1

(sec)

Average time period T1

(sec)

1

2

3

4

5

Table 2: Measuring Amplitude with damping

x0 = ……. mm

No. of

Oscillations

(n)

Sl. No. xn

(mm)

xn/x0

ln (xn/x0)

2 1

2

3

4 4

5

6

..

Graph: Plot n vs ln x0

Slope = …..

Calculations: τ = ……

γ = …..

Estimation of error:

Precautions:

1. Avoid parallax error while noting the amplitude.

2. Mark the amplitude carefully on the graph sheet pasted on the mirror without disturbing

the set up.

Horizontal component of Earth’s magnetic field ( ) using a Tangent

Galvanometer

AIM: To determine the horizontal component () of the earth’s field.

APPARATUS: (1) Graduated Compass (2) Current carrying coil (3) Rheostat (4) power supply

(5) switch for changing direction of current (6) Ammeter(Digital Multimeter) (7) spirit level

THEORY:

The horizontal component of earth's magnetic field, BH, is the projection of earth's magnetic field

on surface of the earth. Earth’s magnetic field varies with longitude and latitude. Horizontal

component of earth’s magnetic field (BH) in Bhubaneswar is 39 uT. To know magnetic field on a

given location visit this link. http://www.ngdc.noaa.gov/geomag-web/#igrfwmm

Tangent law

Consider a bar magnet with magnetic moment M, suspended horizontally in a region where there

are two perpendicular horizontal magnetic fields, and external field B and the horizontal

component of the earth’s field BH. If no external magnetic field B is present, the bar magnet will

align with BH. Due to the field B, the magnet experiences a torque , called the deflecting

torque, which tends to deflect it from its original orientation parallel to BH. If θ is the angle

between the bar magnet and BH, the magnitude of the deflecting torque will be,

The bar magnet experiences a torque due to the field BH which tends to restore it to its original

orientation parallel to BH. This torque is known as the restoring torque, and it has magnitude.

The suspended magnet is in equilibrium when,

Rearranging gives ------(1)

The above relation, called the tangent law, gives the equilibrium orientation of a magnet

suspended in a region with two mutually perpendicular fields.

Tangent Galvanometer:

A tangent galvanometer works based on Tangent law. It consists of a number of turns of copper

wire wound on a hoop. At the center of the hoop a compass is mounted. When a direct current

flows through the wires, a magnetic field is induced in the space surrounding the loops of wire.

This magnetic flux is designated by Bi. The strength of the magnetic field induced by the current

at the center of the loops of wire is given by Amperes law:

Induced

. --------(2)

where µ0 is the permeability of free space and has the value of 4x 10-7

Newton/Amp2, N is the number of

turns of wire, ‘i’ is the current through the wire, and R is the radius of the loop.

When the wire loops of the tangent galvanometer are aligned with the magnetic field direction of

the Earth, and a current is sent through the wire loops, then the compass needle will align with the vector

sum of the field of the Earth and the induced field as shown in Figure 1.

B of Earth

Magnetic

North

Compass Needle

Direction

θ

Bi (induced)

Bresultant

Fig. 1

Tangent

Galvanometer

A

Rheostat

Reversing

Switch

Fig. 2: CIRCUIT DIAGRAM

The horizontal component of the magnetic field of the Earth (BH) is calculated from the

following relation:

--------------(3)

Diameter of the coil (R) = 13.6 cm.

Procedure:

1. Level the graduated compass by a spirit level and also see that the current carrying coil is

vertically placed.

2. Set the compass needle to 0-0 position. If there is offset in the pointer in the needle note

down the value.

3. Connect the power supply, rheostat, ammeter and reversing switch as per the circuit

diagram.

4. Connect the current carrying coil from the reversing switch to 50 turns position.

5. Always set the rheostat in middle position.

6. Slowly vary the power supply to set current in the ammeter (connect the digital

multimeter in mA range with DC mode).

7. Note down the deflection in the compass for both left and right direction.

8. Always try to take observations in the range of 15°-75° in the compass.

9. Turn the power supply to initial position, then reverse the current direction at the

reversing switch and repeat the measurements (use same current values).

10. After completing for 50 turns, follow the same procedure for the 500 turns position of the

coil.

11. Compare the obtained magnetic field with Horizontal component of magnetic field at

Bhubaneswar.

Table 1: For 50 turns

Current

(mA)

Deflection of compass Deflection of compass

by reversing current

direction

Bi (Tesla) BH (Tesla)

Left Right Left Right

Table 2: For 500 turns

Current

(mA)

Deflection of compass Deflection of compass

by reversing current

direction

Bi (Tesla) BH (Tesla)

Left Right Left Right

Results:

1

Magnetic field variation along the axis of a circular coil and a Helmholtz coil

Aim: 1) To study the variation of magnetic field along the axis of a circular coil

2) To study the principle of superimposition of magnetic field using a Helmholtz coil

Apparatus:

Constant current Power supply DC 0-16 V, 5 Amp, Digital Gauss meter with Axial Hall Probe

(Transducer), Current carrying coil with 390 turns (N), Diameter 150 mm, support base and

stand, Deflection compass, multimeter and connecting leads

Theory: The intensity of magnetic field at a point ‘P’, lying on the axis of a circular coil ‘AB’

or radius ‘a’ having ‘n’ turns at a distance ‘x’ from the centre ‘O’ of the coil in S.I. units, is given

by

4

·2

⁄

Where I is the current flowing through the coil, µ0 is the permeability of free space, which is

equal to 4π·10-7

H/m.

Fig. 1

The direction of the magnetic intensity at P is along OP if the current flows through the coil in

the anti-clock-wise direction as seen from P. If the direction of the current is clockwise the field

at P is along PO.

The value of the magnetic intensity is maximum at the centre of the coil and is given by

4

·2

2

Fig.2

If we move away from O towards the right or left, the intensity of the magnetic field

decreases. A graph showing the relation between the intensity of the magnetic field B and the

distance x is given in Fig.2. The curve is first concave (towards O) but the curvature becomes

less and less, quickly changes sign at P and Q and afterwards becomes convex towards O. It can

be shown that the points of inflexion P or Q where the curvature changes its sing lie at distances

‘a/2’ from the centre. Hence the distance between P and Q id equal to the radius of the coil.

A pair of current carrying coils connected in series and separated by radius of the coils is

known as Helmholtz coil. Helmholtz coil produces a uniform magnetic field between the coils,

which is given by

xR

NIB o ˆ

125

8µ=

v

Procedure

i. Using spirit level verify and adjust that track for moving the Hall probe is horizontal and

track is at the centre of the current carrying coils.

ii. Connect the DC supply, Ammeter (Multimeter in current mode), first circular coil in

series as shown in the figure 3. Get the circuit checked by T.A. before switching on

the power supply.

iii. Adjust zero knob such that magnetic feild is zero at the centre of the coil without

switching on the power supply.

3

iv. Switch ‘ON’ the DC supply. Rotate the current knob to 1/3 rd of full movement and then

increase the voltage. Check the current. Increase the voltage till current is 0.5 Amp. If

needed, rotate current know slightly to get 0.5 Amp.

v. Note that current should be constant throughout the experiment. Check it before

taking each reading in the multimeter.

vi. You are provided with an axial Hall probe connected to a Gauss meter. End portion of

the probe detects magnetic field. Move it to centre of the coil and check the position at

which magnetic field is maximum.

vii. Place the given compass on the track and find the direction of magnetic field. Then

determine the current direction in your coil (clock wise/Anticlock wise)

viii. Remove the compass from the track and move the Hall sensor to 10 cm left of the left

coil.

ix. Take readings of magnetic field for each 0.5 cm from 10 cm left to 10 cm right of the

coil and tabulate. Magnetic field in Gauss meter fluctuates due to electronics used. At

each step, wait for few seconds and note down the average value.

x. Switch off the supply and place the second coil at a distance equal to radius of the coil.

xi. Disconnect the first coil and make connections to second coil and repeat the

measurement as above.

xii. Third measurement is for Helmholtz coil setup. Make connections as in Figure 2. Check

with compass that magnetic field is in same direction for both the coils.

xiii. Measure magnetic field from 10 cm left of the first coil to 10 cm right of the second coil

for each 0.5 cm.

xiv. Draw the graphs between distance and magnetic field due to COIL 1, COIL 2 and

BOTH along the axis of coils in a single graph and estimate the radius of the coil.

xv. Calculate the radius of coil to verify with the given value

where B is field of the coil the centre of the coil.

xvi. Calculate magnetic field at the centre of the Helmholtz coil using xR

NIB o ˆ

125

8µ=

v

4

Fig. 3: Experimental Arrangement for single coil

Fig.4: Experimental Arrangement for Helmholtz coil

0-16 V DC

A

Coil 1 Coil 2

Coil 1 0-16 V DC

A

5

Observations

Precautions

1) Care should be taken that there is no stray magnetic field or ferromagnetic material,

such as keys, screwdriver etc. near the setup, while performing the experiment.

2) The radius of the coil is calculated from the centre of winding and not from the

inside edge of the coil bobbin.

3) The Zero of the Gauss meter should be adjusted each time before beginning the

experiments and verified after the completion of experiment by reducing the current

in both the COILS to zero.

Questions: 1) What is a solenoid? What is the variation of magnetic field along the axis of

solenoid?

Sensor

position

(cm)

COIL 1 field

(Gauss)

COIL-2 field

(Gauss)

Both coils field

(Gauss)

Helmholtz

arrangement

Resolving Power of a telescope with a rectangular aperture

Objective:

• To determine the resolving power of a telescope with a rectangular aperture

Apparatus:

Telescope, variable rectangular slit, Na lamp, source slits

Theoretical background:

A simple telescope consists of a large aperture objective lens with high focal length and

an eye piece with a lower focal length and smaller aperture. An eye piece consists of two lenses

separated a distance. The lens towards the objective is called the field lens and other which is

near to the eye is known as eye lens.

The resolving power of an optical instrument, say a telescope or microscope, is its ability

to produce separate images of two closely spaced objects/ sources. The plane waves from each

source after passing through an aperture from diffraction pattern characteristics of the aperture. It

is the overlapping of diffraction patterns formed by two sources sets a theoretical upper limit to

the resolving power.

Consider two narrow slit sources, d distance apart, kept at a distance D away from the

aperture, i.e. objective, of a telescope. In the following we will stick to rectangular aperture.

Then the angular separation α of the slits at the aperture is α = d/D. Each slit will produce its own

single slit diffraction pattern, for which the intensity distribution is given by,

, where

(1)

And is the slit width, θ is the angle of diffraction and λ is the wave length of light from the

sources. The principal maximum of each slit corresponds to θ = 0 0 and the position of

the minima, which are points of zero intensity, corresponds to , 2 etc. The angular

separation of the two principal maxima is equal to the angular separation of the sources, i.e. α.

The Rayleigh’s criterion for resolution of two diffraction patterns states that two sources

or their diffraction patterns are resolved when the principal maximum of one falls exactly on the

first minimum of the other. Since the first minimum is formed at , then angular separation

α of the maxima is equal to the corresponding θ1,

sin

(2)

The angle is known as minimum angle of resolution while 1 "is sometimes called the

resolving power of the aperture . For circular aperture, Rayleigh’s criterion is modified to

1.22 $ " . To find the intensity at the centre of the resultant minimum for the overlapping

diffraction fringes separated by , we note the curves of principal maxima cross at 2" for

either pattern. Therefore intensity at the centre, relative to the maximum, is sum of the intensity

of either at 2" ,

%& '

%( 2 )

*

0.8106 (3)

Procedure:

1. Make the axis of the telescope horizontal by adjusting it with a spirit level and its height is to

be adjusted that the images of the pair of slits are symmetrical with respect to the cross point of

the cross wires.

2. The images are brought into sharp focus by adjusting the telescope while keeping the variable

aperture wide open.

3. Reduce the width of the aperture gradually so that at first the two images appear out and

ultimately their separation vanishes. Measure the width of the aperture at this critical position.

Reducing aperture further and

note the reading when the illumination (light) just disappears altogether. The difference of these

two readings gives width of the aperture required.

4. Now begin with a closed aperture gradually increasing the width. Take the first reading when

the illumination just appears and then when the two images just appear to be separated. The

difference giving the width of the aperture is noted.

5. Repeat the operation 3 and 4 for three or four times.

6. Measure the distance between the slits (sources) and the objective of the telescope by means

of measuring tape.

7. Observe that as you increase the distance D between the telescope aperture and source for a

fixed d and λ, you need larger aperture to resolve the two sources. It is needless to mention that

larger aperture implies larger light gathering capacity.

For fun, you can test how good the resolving power of your eyes are by looking at the second

star from the tip of the handle of Big Dipper or saptarshi mandal in the constellation of Ursa

major. The name of the bright star is Mizar

(vasistha), but it has a faint optical companion called Alcor (Arundhati) and the ability to resolve

the two stars with naked eye is often quoted as a test of eyesight.

8. Observe the construction of telescope. What are the components used in the telescope? Pull

out the eye piece and observe the location of cross wires. Which type of eye piece is used in the

telescope? Ramsden’s or Huyghen’s? What is the difference between these two types of

eyepieces?

Fig. 1 Experimental setup

Observations

Determination of least count of the traveling microscope

Value of smallest main scale division (MSD) = ……………………………

…………………….vernier scale division = ………………………..main scale division

Hence, 1 vernier scale division = …………………………main scale division (VSD)

Vernier Constant (VC) = (1 – VSD) x MSD = …………………………….m

Table-I. Determination of the source slits separation d

Slit edge

obs

Left slit Right slit d (m) Mean d

Mai

n s

cale

(M

)

Ver

nie

r (V

)

T =

M +

VC

x V

Mea

n T

Mai

n s

cale

(M

)

Ver

nie

r (V

)

T =

M +

VC

x V

Mea

n T

L

1

2

3

-=

- -~ /

………

R

1

2

3

/=

/ /~ -

Least count of screw gauge attached to the aperture

Value of smallest main scale division (MSD) = ……………………………

Number of circular scale division (CD) = …………………………………….

Screw Pitch (P) = 1/CD = ……………………Least Count (LC) = P x MSD = ………....m

Table II. Determination of minimum angle of resolution θ1 at varying D

Wavelength of light used λ = 589.3 x 10-9

m. Average source slits separation d = ……….m

Obs D (m) 0

1

Open slit

circular scale

(C0)

Closed slit

circular scale

(C1)

Number of

rotated

division

N)

2 ) 34 &5'

$

(radian)

1a

1b

1c

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

6a

6b

6c

Plot the 6 graph, explain why it gets difficult to achieve increasingly low ?

Questions

1. How the minimum angle of resolution changes with the wavelength of the light $?

2. Which one of the two telescopes, optical and radio has more resolving power for a given

aperture?

3. What is the for human eye for red (700nm), yellow (600nm), and blue (400nm) light,

assuming dark-adapted average pupil size is 5mm? (Use the Rayleigh’s criterion for

circular aperture.)

1

Dispersion of light by a prism

Aim: (i) To calculate refractive index µ of a prism for various wavelengths (λ) of Hg and to find

dispersive power of the material of the prism.

(ii) To plot µ-1/λ2 curve and hence determine Cauchy’s constants for the prism material.

Apparatus: Spectrometer, prism, Hg lamp and spirit level

Theoretical background

When a ray of light is refracted by a prism, the angle between the incident and refracted ray is

called the angle of deviation δ. For a given prism angle A and wavelength λ, δ depends on the

angles of incidence i and emergence r (See Fig. 1). The angle of deviation is minimum when the

angles of incidence i and emergence r make equal angles with prism surfaces, i.e. i= r. We

denote this angle of minimum deviation as δm which depends on the wavelength of the light used.

Refractive index of the prism for a given wavelength of light λ is related to the corresponding δm

by,

(1)

If µ1 and µ2 are refractive indices of the material

of the prism for wavelengths λ1 and λ2, and µ is

the refractive index of λ, which is the mean of λ1

and λ2, then dispersive power is defined as

(2)

Using Eq.(1), µ(λ) of the prism can be obtained experimentally by determining δm for the

corresponding λ. Thus a calibration curve of µ-λ can be drawn for the prism from which the

refractive index can be determined for a given wavelength or vice-versa. The experimental µ-λ

curve can be described with a fair degree of accuracy by the empirical Cauchy’s equation,

, (3)

where C and D are Cauchy’s constants for the prism material. The plot µ versus 1/λ2

is a straight

line from which C and D values can be determined by fitting the data with Cauchy’s relation.

The dispersion of the material of the prism is defined as ⁄ , which can be obtained from the

Cauchy’s formula in eqn. (2),

!" , (4)

Fig. 1

Experimental set up:

In this experiment, we will use a prism

various wavelengths. The detail description of the spectrometer is already provided as a separate

note. Before starting the experiment please identify all parts of the spectrometer. Familiarize

yourself with the focusing adjustments and also coarse and fine movement of different parts.

Procedure:

1. DO NOT PLACE THE PRISM ON THE SPECTROMETER YET.

2. First check leveling of the spectrometer

needed, level them using the adjustment screws and a spirit level.

3. The collimator is adjusted for parallel beam of light and the telescope for focusing the

parallel beam by Schuster’s method (details of which is given i

present set up may not require it.

4. Adjusting the telescope: While looking through the telescope, slide the eyepiece in and out

until the crosswire comes into sharp focus. Point the telescope at some distant object and

view it through the telescope. Turn the focus knob of telescope until the image is sharp. The

telescope is now focused for parallel light rays.

henceforth.

5. Ensure the Hg lamp is fully illuminated and placed close to the sl

that the slit is partially open.

6. Adjusting the collimator:

through the telescope, to see a focused image of the slit. If necessary, adjust the slit width

2

In this experiment, we will use a prism spectrometer to measure the deviations of light

The detail description of the spectrometer is already provided as a separate

note. Before starting the experiment please identify all parts of the spectrometer. Familiarize

ith the focusing adjustments and also coarse and fine movement of different parts.

Fig. 2: Experimental set up

DO NOT PLACE THE PRISM ON THE SPECTROMETER YET.

the spectrometer base, prism table, collimator and telescope

using the adjustment screws and a spirit level.

The collimator is adjusted for parallel beam of light and the telescope for focusing the

parallel beam by Schuster’s method (details of which is given in another experiment). But the

not require it.

While looking through the telescope, slide the eyepiece in and out

until the crosswire comes into sharp focus. Point the telescope at some distant object and

through the telescope. Turn the focus knob of telescope until the image is sharp. The

telescope is now focused for parallel light rays. DO NOT change the focus of the telescope

Ensure the Hg lamp is fully illuminated and placed close to the slit of the collimator. Check

Align the telescope directly opposite the collimator and look

through the telescope, to see a focused image of the slit. If necessary, adjust the slit width

spectrometer to measure the deviations of light for

The detail description of the spectrometer is already provided as a separate

note. Before starting the experiment please identify all parts of the spectrometer. Familiarize

ith the focusing adjustments and also coarse and fine movement of different parts.

table, collimator and telescope. If

The collimator is adjusted for parallel beam of light and the telescope for focusing the

n another experiment). But the

While looking through the telescope, slide the eyepiece in and out

until the crosswire comes into sharp focus. Point the telescope at some distant object and

through the telescope. Turn the focus knob of telescope until the image is sharp. The

DO NOT change the focus of the telescope

it of the collimator. Check

Align the telescope directly opposite the collimator and look

through the telescope, to see a focused image of the slit. If necessary, adjust the slit width

3

until the image of the slit as seen through the telescope is sharply focused on the crosswire.

The collimator is then set to produce parallel light from the slit.

7. Determine the vernier constant of the spectrometer. Report all the angles in degree unit.

Details about reading angles in spectrometer are given in the manual for finding angle of

minimum deviation.

8. Angle of prism: (Refer Fig. 2)

• Place the prism such that its vertex is at the center

of the prism table, directly in line with the

illuminated slit.

• The opaque face (AC) should face towards you so

that light from the collimator is reflected at the

two faces AB and AC.

• Rotate and adjust the telescope to position I where

the image of the slit reflected at AB is centered on

the crosswire. Record the angular positions on

each vernier.

• Now, turn the telescope to position II for the

image reflected at AC and record again the

angular positions on each vernier.

• Take three independent sets of readings for

telescope position I and II on each vernier. Let the

mean of these three sets of readings of the two

verniers V1 and V2 are respectively,

telescope position I: α1 , α2

telescope position II: β1 , β2

• Then the mean angle of the prism A is obtained using

#$ $% $#/#, where ' (~* and '! (!~*!.

9. Direct ray reading: Remove the prism from the

spectrometer and align the telescope so that the direct

image of the slit is seen through the telescope centered

on the crosswire. Record the angular position of the

telescope on the two verniers as D1 and D2. This will be

the reference angular position for any measurements

later.

10. Angle of minimum deviation: (Refer Fig. 3)

• Replace the prism on the spectrometer table so that it is

oriented as shown in Fig. 3.

• Locate the image of the spectrum with naked eye. Then

rotate the telescope to bring the spectrum in the field of

view.

• Gently turn the prism table back and forth. As you do so,

the spectrum should appear to migrate in one direction

until a point at which it reverses its direction.

• Lock the prism table. Now, using fine adjustment screw

Telescope

Position-II Telescope

Position-I

Fig. 2

Fig. 3

4

of the telescope fix the crosswire on one of the spectral lines of wavelength λ1 at an extreme

end.

• Then move the prism table using fine adjustment screw so that the angle where the line starts

reversing its direction is precisely located. Take three such independent readings. Let the

mean of these readings on the two verniers V1 and V2 for λ1 are θ1 and θ'1. Calculate the mean

value of δm(λ1) as follows:

δmλ 12 0θ~D θ3~D!4

• Similarly, note down the angles of minimum deviation for all the spectral lines, whose

wavelengths and colors are given in the chart. (see last page)

11. Calculate the refractive index for each wavelength using Eq.1 and then determine the

dispersive power using Eq. 2.

12. Plot µ ~ (1/ λ2) and determine Cauchy’s constants by least square fitting.

OBSERVATIONS

Table 1: Determination of vernier constant (VC) of the spectrometer

Value of 1 small main scale division (MSD) = ………

……. vernier scale divisions = ….. main scale divisions

Hence, 1 vernier scale division = ………… main scale division (VSD)

Vernier Constant (VC) = (1 – VSD) x MSD = ………

Table-2. Determination of the angle of the prism

Vernier

obs Reflection image1 Reflection image 2 2A (degree) Mean 2A

(degree)

A

(degree)

Mai

n s

cale

(M)

Ver

nie

r (V

)

T =

M +

VC

x V

Mea

n T

(deg

ree)

M

ain s

cale

(M)

Ver

nie

r (V

)

T =

M +

(V

C

x V

)

Mea

n T

(deg

ree)

V1

1

2

3

(=

* ' (~ *

2' ' '! 25

V2

1

2

3

(!=

*! '! (!~ *!

5

Table-2. Direct ray reading

Vernier Obs. Main scale (M) Vernier (V) T = M + (VC x V) Mean (degree)

V1

1

2

3

6

V2

1

2

3

6!

Table-3. Angle of minimum deviation for various λ

Color

/ λ(

nm)

Vernier Obs Main

Scale(M)

Vernier

(V)

T = M + (VC

x V)

Mean

(degree)

δm(λn)

(degree)

Mean δm(λn)

(degree)

Color

V1 1

2

3

θ θ~D

78 ……………

. V2 1

2

3

θ3 θ3~D!

.

.

.

.

.

.

.

.

.

.

.

.

Color

9

V1 1

2

3

θ θ~D

789 …………… V2 1

2

3

θ3 θ3~D!

Table-4. Determination of refractive indices :; and data for : < %/;# plot

angle of the prism, A = ….

Color (nm) 1/! (nm-2

) 78

..

..

..

..

..

..

………..

………..

.

.

.

.

………..

………..

.

.

.

.

………..

………..

.

.

.

.

………..

………..

.

.

.

6

Calculations:

Dispersive power of prism =

Cauchy’s constants: Using least square fitting in < 1/! plot

C = ….. D = ……

Precautions:

1. Do not touch the refracting surfaces by hand. Place the prism on the prism table or remove it

from the prism table by holding it with fingers at the top and bottom faces. The reflecting

surfaces of the prism should be cleaned with a piece of cloth soaked in alcohol.

2. Rotate the adjustment screws slowly. Do not force any movement. If something is not

moving check the clamping screw. Use fine adjustment screw after locking the clamping

screw.

Questions: 1) What is normal and anomalous dispersion? Where do you get anomalous

dispersion?

2) What are the factors on which the dispersive power of a prism depends?

Additional Reading:

1. Feynman lectures on physics, volume 1. Narosa Publishing House, Delhi

2. Practical Physics, R.K. Shukla and A. Srivastava, New Age International (P) Ltd.

1

Newton’s rings

Apparatus:

Traveling microscope, sodium vapour lamp, plano-convex lens, plane glass plate, magnifying

lens.

Purpose of the experiment:

To observe Newton rings formed by the interface of produced by a thin air film and determine

the radius of curvature of a plano-convex lens.

Basic Methodology:

A thin wedge shaped air film is created by placing a plano-convex lens on a flat glass plate. A

monochromatic beam of light is made to fall at almost normal incidence on the arrangement.

Ring like interference fringes are observed in the reflected light. The diameters of the rings are

measured.

I. Introduction:

I.1 The phenomenon of Newton’s rings is an illustration of the interference of light waves

reflected from the opposite surfaces of a thin film of variable thickness. The two interfering

beams, derived from a monochromatic source satisfy the coherence condition for interference.

Ring shaped fringes are produced by the air film existing between a convex surface of a long

focus plano-convex lens and a plane of glass plate.

I.2. Basic Theory:

When a plano-convex lens (L) of long focal length is placed on a plane glass plate (G) , a thin

film of air I enclosed between the lower surface of the lens and upper surface of the glass

plate.(see fig 1). The thickness of the air film is very small at the point of contact and gradually

increases from the center outwards. The fringes produced are concentric circles. With

monochromatic light, bright and dark circular fringes are produced in the air film. When viewed

with the white light, the fringes are coloured.

A horizontal beam of light falls on the glass plate B at an angle of 450. The plate B

reflects a part of incident light towards the air film enclosed by the lens L and plate G. The

reflected beam (see fig 1) from the air film is viewed with a microscope. Interference takes place

and dark and bright circular fringes are produced. This is due to the interference between the

light reflected at the lower surface of the lens and the upper surface of the plate G.

2

For the normal incidence the optical path difference between the two waves is nearly 2µt,

where µ is the refractive index of the film and t is the thickness of the air film. Here an extra

phase difference π occurs for the ray which got reflected from upper surface of the plate G

because the incident beam in this reflection goes from a rarer medium to a denser medium. Thus

the conditions for constructive and destructive interference are (using µ = 1 for air)

2 t = m λ for minima; m =0,1,2,3… … … … … .. -----(1)

and 2 t = (m+1/2λ) for maxima; m = 0,1,2,3… … … … … . -------------(2)

Then the air film enclosed between the spherical surface of R and a plane surface glass plate,

gives circular rings such that (see fig 2)

Fig. 2 Fig. 3

3

If Dm is the diameter of the mth

bright ring from the centre then

2 1

(3)

Where R is the radius of curvature of the plano convex lens, λ is wave length of light. Equation 3

can be written as

22 1 (4)

II. Setup and Procedure:

1. Clean the plate G and lens L thoroughly and put the lens over the plate with the curved surface

below B making angle with G(see fig 1).

2. Switch in the monochromatic light source. This sends a parallel beam of light.

3. Look down vertically from above the lens and see whether the center is well illuminated. On

looking through the microscope, a spot with rings around it can be seen on properly focusing the

microscope.

4. Once good rings are in focus, rotate the eyepiece such that out of the two perpendicular cross

wires, one has its length parallel to the direction of travel of the microscope. Let this cross wire

also passes through the center of the ring system.

5. Now move the microscope to focus on a ring (say, the 20th order dark ring). On one side of

the center. Set the crosswire tangential to one ring as shown in fig 3.

Note down the microscope reading (Make sure that you correctly read the least count of the

vernier in mm units)

6. Move the microscope to make the crosswire tangential to the next ring nearer to the center and

note the reading. Continue with this purpose till you pass through the center. Take readings for

an equal number of rings on the both sides of the center.

Now move the microscope to focus on a ring (say, the 20th

order dark ring). On one side of the

center. Set the crosswire tangential to one ring as shown in fig 3. Note down the microscope

reading.

(Make sure that you correctly read the least count of the vernier in mm units)

4

6. Move the microscope to make the crosswire tangential to the next ring nearer to the center and

note the reading. Continue with this purpose till you pass through the center. Take readings for

an equal number of rings on the both sides of the center.

7. Use Equation 4 to find the Radius ‘R’ of plano convex lens by least square fitting. Wave

length of sodium light (λ) is 5893 Angstrom.

Table: Measurement of the diameter of the rings

Ring

No. (m)

Microscope reading Diameter

Dm=R1~R2

(cm)

Dm2 2(2m+1)

Left reading (R1) Right reading (R2)

1

2

3

..

..

..

..

Precautions:

Notice that as you go away from the central dark spot the fringe width decreases. In order to

minimize the errors in measurement of the diameter of the rings the following precautions should

be taken:

i) The microscope should be parallel to the edge of the glass plate.

ii) If you place the cross wire tangential to the outer side of a perpendicular ring on one side of

the central spot then the cross wire should be placed tangential to the inner side of the same ring

on the other side of the central spot.(See fig 3)

iii) The traveling microscope should move only in one direction to avoid backlash error.

Reference: Practical Physics by R.K. Shukla and A. Srivatsava, New Age International Ltd.

1

Laser Diffraction and Interference

Objective

• To determine the wavelength of laser light from a thin wire diffraction pattern.

• Compare the thickness of the wire with the single-slit width that form the same diffraction

pattern as wire and hence verify the Babinet’s principle.

• To explore the double-slit interference pattern.

Apparatus

Laser source (and safety goggles), screen & ruled-paper for recording, thin-wire source, variable

single-slit and double-slit sources, grating, measuring tape, travelling microscope and (if

available) digital camera

Theoretical background

When light passes through a small opening or around an edge, secondary waves from different

portions of the emerging wavefront will, in general, travel different distances before reaching a

screen. Although the waves from secondary sources are all in phase to start with, they will be

out of phase by the time they reach the screen. The interference of these radiation emitted by

secondary on the wavefront leads to the phenomenon of diffraction. We will study only

Fraunhofer diffraction, where the light source, screen and the object causing diffraction are

effectively at infinite distances from each other.

Single-slit diffraction

When a light of wavelength λ is incident normally on a narrow slit of width b, the resultant

intensity of the transmitted light is given by,

, with (1)

where, θ being the angle of diffraction. The diffraction pattern consists of a principal maximum

for β = 0, where all the secondary wavelets arrive in phase, and several secondary maxima of

diminishing intensity with equally spaced points of zero intensity at β = mπ. The positions of

the minima of a single-slit diffraction pattern are,

mλ = b sin θ, m = ±1, ±2, ±3, . . . .

sin , m = ±1,±2,±3…….. (2)

2

If θ is small i.e. the slit to screen distance D is large compared to the distance xmbetween two

m-th order minima (on either side of principal maximum), then

sin ……(3)

The above equation (3) can be used to determine the wavelength of the monochromatic light

source, laser in present case, by measuring b, D and xm for various m. The positions of the

minima can be obtained by averaging the two extremities of the zero intensity region, as shown

in the picture below.

Figure 1. Single-slit diffraction pattern – distance between minima xm is calculated from the

average minima position on either side of principal maxima.

Diffraction of a thin wire

If the single-slit is replaced by a thin wire obstacle, which blocks as much laser light as a

single-slit will allow to pass, the resulting diffraction pattern will be identical to that of a single-

slit. Knowing the wavelength λ of the laser light, the equation (3) can be used to determine the

thickness of the wire b as,

(4)

A typical diffraction pattern of a wire obstacle is shown below. Here too, the positions of the

minima are calculated by averaging the two ends of the spread of zero intensity regions as shown

in Fig 2.

Figure 2. Diffraction pattern from wire obstacle– similarity with single-slit pattern is what

Babinet’s principle asserts. xm is measured as in single-slit case.

3

The fact that Fraunhofer diffraction pattern due to an obstacle is virtually identical to that of an

opening of same dimension is an example of a general rule called Babinet’s principle. This

principle can be verified by replacing once again the wire with a single- slit and varying the slit-

width until the pattern matches exactly. The slit width can then be compared with the wire

thickness.

Dobule-slit interference

If instead of single-slit, we have two parallel slits each of width b separated by an opaque space

of width c, the corresponding intensity distribution of the Fraunhofer pattern formed is,

cos (5)

Where being the angle of diffraction,

, !

, d= b + c, (6)

The intensity distribution is a product of two terms: the first term (sin2 β/β2) represents

diffraction pattern produced by single-slit (eqn.1) and the second term cos2 γ is the characteristic

of interference produced by two beams of equal intensity and phase difference γ. The overall

pattern, therefore, consists of single-slit diffraction fringes each broken into narrow maxima and

minima of interference fringes. This interference of light from two narrow slits close together

was first demonstrated by Thomas Young in 1801 and helped establish the wave nature of light.

The minima for the interference fringes are at γ = (2p + 1)π/2 with p = 0, 1, 2, . . . and those for

diffraction fringes are at β = mπ where m = 1, 2, 3, . . .. The conditions for minima are,

" sin #$ % &' (7)

sin (8)

A typical double-slit Fraunhofer pattern obtained with laser beam is shown in Fig 3. The

intensity of laser may render viewing the pattern difficult without photographing.

Figure 3. Double-slit interference pattern – each diffraction maxima is broken up into

interference fringes. The minima positions xp (interference) and xm (diffraction) are read off

directly without averaging.

4

Procedure

WARNING: The laser beam can cause real damage to your eyes if you look into the beam

either directly or by reflection from shiny objects.

1. Determine the vernier constant of the travelling microscope and measure the thickness b of

the wire, slit-width b for single and double slit, and slit plus opaque space d = b + c of

double-slit.

2. Arrange the screen at least 2 meter away from the laser source. On the screen, attach a ruled-

paper with clips such that the ruled scale is horizontal. You may use graph paper in place of

ruled-paper, if you consider it convenient.

3. Turn the laser on and be extremely careful not to let your eyes in the direct or reflected line of

the laser. Does not turn the laser off and on too frequently; instead use something to block the

laser when it is not in use.

4. Adjust the height of the laser (and also the screen) such that the laser spot is directly on the

ruled line in the middle of the paper.

5. To record the pattern that will be produced on the screen, mark the fringe pattern with pencil

on edges of bright spots on both left and right side of the central maximum. Calculate the

midpoints of minima and subtract one from other to find fringe width ( )*~),

6. First place a thin wire apparatus close in front of the laser and observe the diffraction pattern

on the screen. Adjust the laser and slit so as to obtain a bright, crisp pattern. Measure the slit to

the screen distance D with a measuring tape. Calculate the wavelength of the laser in use from

the data and equation (3) by straight line fit.

7. Next replace the wire with a single slit and adjust the width of the slit to match the pattern

which was obtained with the wire. Keep the distance between slit and screen same as in the wire

screen distance. Calculate the thickness of the single slit using traveling microscope and compare

the result to the value wire thickness to verify Babinet’s principle.

8. To explore the double-slit pattern, proceed exactly the same way as single-slit, but this time

around it may be difficult to mark off the diffraction minima directly on the screen although the

interference minima are fairly easy to spot. Show the pattern to instructor. You do not need to

take any observations for this part. What type of patterns you expect with multiple slits?

5

Observations and results

Value of smallest main scale division (MSD) = . . . . . .

. . . . . . vernier scale division = . . . . . . main scale division

Hence, 1 vernier scale division = . . . . . . main scale division (VSD)

Vernier constant (VC) = (1 − VSD) × MSD = . . . . . .

Table I. Determination of wire thickness

Ob

ject

Obs

Left edge Right edge

b (

m)

Mea

n b

(m

)

Mai

n S

cale

(M

)

Ver

nie

r (V

)

T =

M +

VC

xV

Mea

n T

Mai

n S

cale

(M

)

Ver

nie

r (V

)

T =

M +

VC

xV

Mea

n T

Wire 1

2

3

αl= αr= αl ~αr

6

Table-II. Determination of wavelength of the laser light

Wire thickness =……. Slit screen distance D=……

Ord

er

Left fringes Right fringes

Fringe

width

( )*~),

(cm)

Left

edge

(cm)

Right

edge

(cm)

Average, )*

(cm)

Left

edge

(cm)

Right

edge

(cm)

Average, ),

(cm)

1

2

3

.

.

.

Plot Xm versus m and by straight line fitting find slope and determine wave length (λ).

Table III. Determination of the single-slit width to prove Babinet’s principle

Ob

ject

Obs

Left edge Right edge

b (

m)

Mea

n b

(m

)

Mai

n S

cale

(M

)

Ver

nie

r (V

)

T =

M +

VC

xV

Mea

n T

Mai

n S

cale

(M

)

Ver

nie

r (V

)

T =

M +

VC

xV

Mea

n T

Single

slit

1

2

3

el = er= el ~ er

7

Questions:

1. In what way interference and diffraction differ?

2. What would you expect if ordinary sodium lamp (supposing it to be monochromatic) is

used instead of laser? What if white light is used?

3. Why the positions for minima are measured instead of maxima in the cases of single-slit,

wire and double-slit pattern? [Hint: the maxima are not in the center of the bright

region.]

4. What is missing order? Do you expect to get one in the present experimental setup?

STUDY OF POLARISATION AND MALUS’S LAW

AIM: To study Polarization of light and verification of Malus’s law.

APPARATUS: Laser (diode/He-Ne), Optical profile bench, analyzer (polarising filter) photo

detector, and digital multimeter attached to an amplifier, mounts for all above components.

THEORY:

Let AA′ be the Polarization planes of the analyzer in the figure given below. If the linearly

polarized light, the vibrating plane of which forms an angle φ with the polarization plane

impinges on the analyzer, only the part

EA=E0cosφ -- (1) will be transmitted.

As the intensity ‘I’ of the light wave is proportional to the square of electric field intensity vector

E, the following relation on (Malus’ law) is obtained.

IA= I0. cos2φ -- (2)

PROCEDURE:

1. Laser should be warmed up for about 15-30 minutes to prevent intensity of fluctuations.

2. Make sure that the photo detector/photocell is totally illuminated when the polarization

filter is set up.

3. The background voltage V0 must be determined with the laser switched off and this must

be subtracted from actual readings.

4. The polarization filter is then rotated in steps of 5° between the filter positions +/- 90°

and note down corresponding photo cell voltage V.

5. Plot (V-V0) Vs φ and determine the angle of polarization of the given laser(θ).

6. Plot cos2

(φ-θ) Vs (V-V0)/(Vmax-V0) and fit the straight line to find slope and verify

Malus’s law.

EA=E0cosφ

EA E0

A’

A

φ

TABULATION:

V0=__________V

Table 1

Sl.

No.

Angular Position of analyzer

in degrees

Photo cell voltage(V)

in volts

V-V0

in volts

1

2

..

..

Angle of polarization of the laser θ = __________

Table 2

Sl. No. cos2

(φ-θ) (V-V0)/(Vmax-V0)

1

2

..

..

PRECAUTIONS:

1. Never look directly into the laser beam.

2. Photocell readings should be taken carefully.

3. Do not change the direction of the laser as it may affect other experiments in the room.

You are allowed only slight adjustment of the direction.