000 Light ENG rev6 20160901 - Yonsei Universityphylab.yonsei.ac.kr/exp_ref/209_Light_ENG.pdf · and...

General Physics Lab (International Campus) Department of PHYSICS YONSEI University

Lab Manual

Interference and Diffraction of LightVer.20160901

Lab Office (Int’l Campus)

Room 301, Building 301 (Libertas Hall B), Yonsei University 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA (☏ +82 32 749 3430) / 15

[International Campus Lab]

Interference and Diffraction of Light

Observe interference and diffraction patterns for various slits and diffraction gratings, and find the wavelengths of laser sources.

Interference and diffraction are the phenomena to show the

wave nature of light. Interference phenomena occur when

two or more waves combine. The colors seen in oil films and

soap bubbles are a result of interference between light re-

flected from the front and back surfaces of a thin film of oil or

soap solution.

When light falls on a straightedge and casts a shadow, the

edge of the shadow is never perfectly sharp. Some light ap-

pears in the area that we expect to be in the shadow, and we

find alternating bright and dark fringes in the illuminated area,

as in Fig. 4. Such effects are referred to as diffraction. There

is no specific, important physical difference between interfer-

ence and diffraction. However, diffraction commonly means

the result from the interference of an infinite number of waves

emitted by a continuous distribution of source points.

1. Interference

Interference is a phenomenon in which two or more waves

superpose to form a resultant wave of greater or lower ampli-

tude.

When waves from two sources arrive at point in phase,

as in Fig. 1(a), they reinforce each other. The amplitude of the

resultant wave is the sum of the amplitudes of the individual

waves. This is called constructive interference. Waves from

the two sources arrive at point exactly a half-cycle out of

phase, as in Fig. 1(b). A crest of one wave meets a trough of

the other wave. The resultant amplitude is the difference be-

tween the two individual amplitudes. This cancellation is

called destructive interference.

Fig. 1 Conditions for constructive and destructive interference.

Objective

Theory

----------------------------- Reference --------------------------

Young & Freedman, University Physics (14th ed.), Pearson, 2016

35.1 Interference and Coherent Sources (p.1184~1187)

35.2 Two-Source Interference of Light (p.1188~1191)

36.2 Diffraction from a Single Slit (p.1212~1215)

36.3 Intensity in the Single-Slit Pattern (p.1215~1219)

36.4 Multiple Slits (p.1219~1221)

36.5 The Diffraction Grating (p.1221~1225)

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Lab Manual




Interference effects are most easily seen when we combine

waves from monochromatic sources of the same frequency

and with a constant phase relationship. We use the term co-

herent light to refer to the light waves emitted by two such

sources.

One of the earliest quantitative experiments to reveal the

interference of light from two sources was performed in 1800

by Thomas Young. Young’s apparatus is shown in perspec-

tive in Fig. 2. A light source emits monochromatic light; how-

ever, this light is not suitable for use in an interference exper-

iment because emissions from different parts of an ordinary

source are not synchronized. To remedy this, the light is di-

rected at a screen with a narrow slit . The light emerging

from the slit originated from only a small region of the light

source; thus behaves more nearly like the idealized

source. (In this experiment, a laser is used as a source of

coherent light, and isn’t needed.) The light from falls

on slits and . Cylindrical wave fronts spread out from

and reach and in phase because they travel equal

distances from . The waves emerging from and are

therefore also always in phase, so and are coherent

sources. The interference of waves from and produc-

es a pattern in space.

Fig. 2 (a) Young’s experiment to show interference of light passing through two slits. (b) Geometrical analysis of Young’s experiment. (c) Approximate geometry when the distance to the screen is much greater than the distance between the slits.

We assume that the distance from the slits to the screen

is so large in comparison to the distance between the slits

that the lines from and to are very nearly parallel,

as in Fig. 2(c). The difference in path length is then given by

sin (1)

Constructive interference occurs at points where the path

difference is an integral number of wavelength, . So the

bright regions on the screen in Fig. 2(a) occur at angle for

which

sin 0, 1, 2, … (2)

Similarly, destructive interference occurs at points for which

the path difference is a half-integral number of wavelengths.

sin12

0, 1, 2, … (3)

Thus the pattern on the screen is a succession of bright and

dark bands parallel to the slits. The intensity at any point can

be expressed in terms of the maximum intensity .

cos2

2

sin (3)

Fig. 3 (a) Photograph of interference fringes produced on a

screen in Young’s double-slit experiment. (b) Intensity distribution in the interference pattern from two identical slits.


Lab Manual




2. Diffraction from a single slit

Diffraction occurs when light strikes a barrier that has an

aperture or an edge. Fig. 4 shows an example of diffraction.

The phenomenon of diffraction can be understood using the

Huygens’s principle, which states that every point on a wave

front acts a source of secondary spherical waves. When the

waves pass through an aperture, each infinitesimal part of the

aperture acts as a source of waves, as shown in Fig. 5(a),

and the resulting pattern of light and dark is a result of inter-

ference among the waves emanating from these sources.

Fig. 4 An example of diffraction

Fig. 5 Diffraction by a single rectangular slit. The long sides of the slit are perpendicular to the figure.

Consider two narrow strips, one just below the top edge of

the slit and one at its center, shown in end view in Fig. 6. The

difference in path length to is 2⁄ sin . If this is equal to

2⁄ , cancellation occurs at . Similarly, the light from every

strip in the top half cancels out the light from a corresponding

strip in the bottom half. Hence a dark fringe occurs whenever

2sin

2or sin (4)

We may also divide the slit into quarters, sixths, and so on,

and use the above argument to show that a dark fringe oc-

curs whenever sin 2 ⁄ , 3 ⁄ , and so on. Thus the

condition for a dark fringe is

sin 1, 2, 3, … (5)

Note that sin 0 0 corresponds to a bright band; in

this case, light from the entire slit arrives at in phase. The

central bright fringe is wider than the others, as Fig. 7. From

Eq. (5) and Fig. 6, we obtain sin ⁄ . If is

much smaller than , is so small that the approximation

sin tan ⁄ is a very good one, and is

∙ ≪ (6)

where is the distance from slit to screen and is the

vertical distance of the th dark band from the center.

Fig. 6 Side view of a horizontal slit. When the distance to the screen is much greater than the slit width , the rays from a distance 2⁄ apart may be consid-ered parallel.


Lab Manual




Fig. 7 shows the diffraction pattern of a single slit. The inten-

sity in single-slit diffraction in terms of the angle is

sin 2⁄

2⁄

2sin (7)

From Eqs. (5) or (7), sin ⁄ . Thus the width of the cen-

tral maximum becomes wider when the slit width decreas-

es, as shown in Fig. 8.

Fig. 7 Intensity versus angle and photograph of the Fraun-hofer pattern in single-slit diffraction.

Fig. 8 The single-slit diffraction pattern depends on the ratio of the slit width to the wavelength .

3. Two Slits of Finite Width

In Figs. 2 and 3 we analyzed interference from two very

narrow slits and . In this analysis we ignored effects

due to the finite (nonzero) slit width. In the more realistic case

in which the slits have finite width, the peaks in the two-slit

interference pattern are modulated by the single slit diffraction

pattern characteristic of the width of each slit.

Fig. 9(a) shows the intensity in a single-slit diffraction pattern

with slit width . The diffraction minima are labeled by the

integer 1, 2, …. Fig. 9(b) shows the pattern formed

by two very narrow slits with distance 4 between slits.

The interference maxima are labeled by the integer

0, 1, 2, ….

Suppose we widen each of the narrow slits forming the pat-

tern of Fig. 9(b) to the same width as that of the single slit

in Fig. 9(a). Then the intensities of the two-slit peaks are

modulated by the single-slit pattern, which acts as an enve-

lope for the intensity function, as in Fig. 9(c). So the intensity

in Fig. 9(c) is proportional to the product of Eqs. (3) and (7):

cos2sin 2⁄

2⁄ (8)

2

sin 2

sin

Fig. 9 Finding the intensity pattern for two slits of finite width.


Lab Manual




4. Several Slits and Diffraction Grating

Fig. 10 shows an array of several narrow slits, with distance

between adjacent slits. Constructive interference occurs for

rays at angle to the normal that arrive at point with a

path difference between adjacent slits equal to an integer

number of wavelengths:

sin 0, 1, 2, … (9)

Fig 10 Multiple-slit diffraction.

Fig. 11 Interference patterns for equally spaced, very narrow slits. (a) Two slits. (b) Eight slits. (c) Sixteen slits. The vertical scales are different for each other.

is the maximum intensity for a single slit, and the maximum intensity for slits is . The width of each peak is proportional to 1⁄ .

Equation (9) shows that the maxima in the pattern occur at

the same positions as for two slits with the same spacing.

However, while there is exactly one intensity minimum be-

tween each pair of maxima in the two-slit pattern, there are

not the only minima in the multiple-slit pattern, as in Fig. 11.

For example, the intensity with eight slits is zero whenever

the phase difference is an integer multiple of 4⁄ , except

when is a multiple of 2 (Fig. 12). Thus there are seven

minima for every maximum as in Fig. 11(b).

When there are slits, there are 1 minima between

each pair of principal maxima. The height of each principal

maximum is proportional to and the width of each maxi-

mum is proportional to 1⁄ . Increasing the number of slits

with keeping the spacing of adjacent slits constant gives in-

terference patterns progressively narrower, so their angular

position can be measured to very high precision.

An array of a large number of slits is called a diffraction

grating. When a grating is illuminated by light, the pattern is

a series of very sharp lines at angle determined by Eq. (9).

So diffraction gratings are widely used to measure the spec-

trum of light emitted by a source.

Fig. 12 Phasor diagrams for light passing through eight narrow slits. Intensity maxima occur when the phase difference 0, 2π, 4π,…. Between the maxima at

0 and 2π are seven minima, correspond-ing to 4⁄ , 2⁄ , 3 4⁄ , , 5 4⁄ , 3 2⁄ , and 7 4⁄ .


Lab Manual




1. List

Item(s) Qty. Description

PC / Capstone software

1 Records, displays and analyzes the data measured by

various sensors.

Interface

1

Data acquisition interface designed for use with various

sensors, including power supplies which provide up to

15 watts of power.

Rotary Motion Sensor

1

Measures angles, angular velocities, etc. of a rotational

motion, and using additional accessories, measures

position, velocities. etc. of a linear motion.

Light Sensor

(Post and DIN Cable included)

1 set Measures relative light intensity.

Laser sources

(Power Adaptor included)

1 set

Emits light with a very narrow spectrum.

Red : 650nm

Green : 532 nm

Optics Bench 1 Provides stable support for holders.

Holder

Mount

(Two Thumbscrews included)

2 sets Provides stable support for optical components.

Linear Stage (Thumbscrew & Square Nut, Two Thumbscrews (for fixing Rack) included)

1 Builds a linear positioning mechanism for scanning the

light intensity of interference patterns.

Rack

1

Converts a linear motion to a rotational motion in com-

bination with the pinion gear inside the Rotary Motion

Sensor.

Equipment


Lab Manual




Items Qty. Description

Aperture Bracket

1 Acts as a mask and holder for the Light Sensor.

Slits

1 Contains several slits.

Diffraction Grating

1 set An array of a large number of parallel slits

Line spacing: 300 lines/mm, 600lines/mm

Ruler Screen

1 Black screen for observing interference patterns of dif-

fraction gratings.

2. Details

(1) Rotary Motion Sensor

The Rotary Motion Sensor is a bidirectional angle sensor

designed to measure rotational or linear position, velocity

and acceleration. (Refer to the manual of the magnetic field

experiment.)

(2) Light Sensor

The Light Sensor makes measurements of relative light

intensity using Si PIN photodiode. It is responsive across a

wide spectrum ranging from 320nm through 1100nm.

(3) Aperture Mask / Slits

Aperture Mask: narrow 1 → 6 wide

Slits:

Slit Width mm / Separation mm

Single Slits 0.02 0.04 0.08 0.16

Variable S.S. 0.02 ~ 0.20

Double Slits 0.04 / 0.25 0.04 / 0.50 0.08 / 0.25 0.08 / 0.50

Variable D.S. 0.04 / 0.125 ~ 0.75

(4) Diffraction Grating

300lines/mm, 600lines/mm


Lab Manual




Setup1. Equipment Setup

(1) Mount the Linear Stage on the left end of the optics bench

Insert the square nut in the center hole of the Linear Stage

into the T-slot located along the center of the Optics Bench.

Tighten the thumbscrew to secure the Linear Stage in posi-

tion.

(2) Mount the Rotary Motion Sensor on the Rack of the stage.

Insert the Rack into the T-slot on the side of the Rotary Mo-

tion Sensor. The teeth on the Rack go through T-slot and then

engage the gear that is on the shaft of the Rotary Motion

Sensor. Place the Rack with the senor back onto the wide

hole of the stage and tighten its thumbscrew.

(3) Use the post to fasten the Light Sensor to the aperture.

(4) Attach the Light Sensor to the Rotary Motion Sensor.

Secure the post of the Light Sensor assembly in the clamp

of the Rotary Motion Sensor. Adjust the height of the Light

Sensor assembly not to touch the pulley of the Rotary Motion

Sensor.

(5) Mount the laser on the right end of the Optics Bench.

(6) Mount the slit disk.

Attach the slit disk to the holder and mount the slit assembly

right in front of the laser with the printed side toward the laser.

Setup


Lab Manual




(7) Plug the sensors into the inputs of the interface.

(9) Set the sensitivity of the Light Sensor.

Set the Light Sensor for maximum sensitivity by sliding

[GAIN] to 100 0~5lux . If the measured light intensity

goes too high (flat line at 100% on the graph), adjust it to

10 0~50lux or 1 0~500lux . Note that lowering the

sensitivity makes the resolution of readings worse.

(10) Select an aperture.

It is recommended to use aperture #2. If required, you can

use any other aperture. If you use a narrower aperture, it is

difficult to observe the light with low intensity. If you use a

wider aperture, measured light intensity goes too high.

(11) Select a slit.

Slit Width mm / Separation mm

Single Slits 0.02 0.04 0.08 0.16

Variable S.S. 0.02 ~ 0.20

Double Slits 0.04 / 0.25 0.04 / 0.50 0.08 / 0.25 0.08 / 0.50

Variable D.S. 0.04 / 0.125 ~ 0.75

(12) Align the laser beam.

Move the sensor assembly until you can see the beam on

the aperture mask. Use the adjustment screws on the laser to

adjust the position of laser beam to pass the slit and to make

the pattern on the aperture as bright as possible.

Caution

The laser beam is so concentrated that it can cause real

damage to your retina if you look into the beam either

directly or by reflection from a shiny object. Do NOT shine

them at others or yourself.


Lab Manual




Setup2. Software (Capstone) Setup

(1) Add sensors.

The interface automatically recognizes the Rotary Motion

Sensor.

Click the input port which you plugged the Light Sensor into

and select [Light Sensor] (yellow icon) from the list.

(2) Configure the Rotary Motion Sensor.

Click the Rotary Motion Sensor icon and then click the prop-

erties button (☼).

Select [Rack & Pinion] for [Linear Accessory].

[Change Sign] switches the sign on the sensor. The sign of

collected data depends on the setup status or the rotational

direction of the shaft. Activate [Change Sign] if required.

(3) Adjust the sample rate of measurements.

Select [20.00Hz] for all sensors, or other value if required.

(4) Create a graph display.

Click and drag the [Graph] icon from the [Displays] palette

into the workbook page. Select [Position(m)] of the Rotary

Motion Sensor for the -axis and [Light Intensity(%)] of the

Light Sensor for the -axis.


Lab Manual




Experiment 1. Diffraction from a Single Slit

(1) Set up your equipment. (See Setup 1.)

(2) Set up the Capstone program. (See Setup 2.)

(3) Select a slit and record the width of the slit.

________ m

(4) Measure the distance between the slit (front side of slit

disk) and the aperture mask.

________ m

(5) Scan the interference pattern.

Click [Record].

Then slowly turn the pulley of the Rotary Motion Sensor to

scan the pattern. Hold the rear of the Rotary Motion Sensor

down against the linear stage bracket so it does not wobble

up and down as it moves.

Click [Stop] when you have finished the scan.

(6) Scale the graph.

Adjust the scale of the graph by clicking [Scale axes…] or by

dragging the mouse pointer on the graph.

Procedure

Caution

The laser beam is so concentrated that it can cause real

damage to your retina if you look into the beam either

directly or by reflection from a shiny object. Do NOT shine

them at others or yourself.

Note

If measured light intensity goes too high (it will flat line at

100% on the graph),

① Place the slit and the sensor assembly as far away as

possible.

② Choose a narrower aperture. (Note that you may not

be able to measure the light of low intensity if the aper-

ture is too narrow.)

③ Change [GAIN] switch on the Light Sensor from

100 0~5lux to 10 0~50lux . (In this case, the

resolution of readings becomes worse.)


Lab Manual




(7) Analyze the graph.

Click [Show coordinates…] to read off data points.

(8) Record your data and analyze the result.

Slit↔Pattern

m

↔ min

m

sin

⁄ sin

1

2

3

average

650nm red 532nm green reference

(9) Repeat the steps (5)-(8) for the other single-slits.

(10) Repeat the steps (3)-(9) for the other laser source.

(11) Repeat for the variable single slit.

Using your eyes, make an observation of changes in pattern

as you decrease the slit width.

Q

How does the single slit pattern change as you decrease

the slit width? What is expected if the slit width decreases

to the light wavelength level? (Refer to Eqs. (5), (7) and

Fig. 8.)

A

Note

You can modify the properties of the graph if required.

Note

The manufacturer of the slits claims the uncertainty in

the slit width is 0.005mm. This means the % uncertainty

in using the 0.02mm slit width is 20% and for the

0.16mm slit width is 3%.


Lab Manual




Experiment 2. Diffraction from Two Slits

Repeat Experiment 1 for double-slits.

Slit↔Pattern

m

↔ max

m

sin

⁄ sin

1

2

3

average


Q Your graph may be different from Fig. 3. Explain why.

A

Q Compare the patterns of different slit widths (same slit

separations) and explain why.

A

Q What is expected if the slit width decreases to the light

wavelength level?

A

Q

Compare the patterns of different slit separations (same

slit widths). Also, when you use the variable double-slit,

how does the pattern change as you decrease the slit

separation? Describe the changes and explain why.

A

Note

The manufacturer of the slits claims the uncertainty in

the slit separation is 0.01mm. This means the % uncer-

tainty in using the 0.25mm slit separation is 4% and

for the 0.50mm slit separation is 2%.


Lab Manual




Experiment 3. Diffraction Grating

(1) Set up your equipment.

Mount the laser, the diffraction grating, and the ruler screen

on the optics bench.

(2) Calculate the slit (line) separation of the diffraction grating.

________ m

(3) Measure the distance between the grating and the screen.

________ m

(4) Measure the distance from the central maximum to the

first maximum.

(5) Record your data and analyze the result.

separation

grating↔screen

m

↔1 max

m

sin

⁄ sin


(6) Repeat the steps (2)-(5) for the other diffraction grating.

(7) Repeat the steps (2)-(6) for the other laser source.

Caution

Handle the diffraction gratings with care. They are very

fragile.

Note

If you cannot find the first maximum on the screen,

check the following.

① If the screen is too far from the diffraction grating, the

first maximum reaches out of the screen. Place the

screen near the grating.

② When the angle is too large, the first maximum

reaches inside surface of the holder. Attach the diffraction

grating on the screen-facing side of the holder.


Lab Manual




Your TA will inform you of the guidelines for writing the laboratory report during the lecture.

Please put your equipment in order as shown below.

□ Delete your data files and empty the trash can from the lab computer.

□ Turn off the Computer and the Interface.

□ Unplug the dc Adaptor of the laser source.

□ Handle the Diffraction Gratings with care. They are very fragile.

□ Tighten all Thumbscrews and Nuts in position.

Result & Discussion

End of LAB Checklist

000 Light ENG rev6 20160901 - Yonsei Universityphylab.yonsei.ac.kr/exp_ref/209_Light_ENG.pdf · and...

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