Hollow Prisms in which liquids are filled form Liquid Prisms.

Prisms form an important class of optical elements. Prisms made of glass or quartz are used in a variety of instruments to change the direction of light. Periscopes contain prisms right angle to its original direction. In binoculars, the direction of the light is reversed after the light is reflected off the two sides of prism.

Prisms also change the direction of a beam of light by means of refraction, i.e. they can bend the light as it passes through them. The angle at which light is refracted depends on its wavelength. Different colours of light have different wavelengths. If a beam of white light, which contains all the wavelengths of visible light, passes through a prism, it is split up to form a band of colours called spectrum. For this reason, prisms are an important part of spectrometers and other instruments that are used to measure the spectral composition of light.

DERIVATION

ABC is the base of an equilateral prism of refracting angle 60.PQ is an incident ray, which gets refracted at the two faces of the prism and finally emerges out along RS.

From QMR, r + r + M = 180 ------ (1)

From QMR, A + M = 180 ------ (2)

From 1 and 2, r + r = A ------- (3)

From QNR,

= i +e r r = i e (r+ r) = i e A ------- (4)

At minimum deviation position i.e. when = m,

r = r = r

and, i e

(3) 2r = A

= r = A/2

(4) m= 2i A

i (A + m ) 2

By Snell’s Law of Refraction,

prism = sin i sin r

= sin (A + m / 2 ) sin ( A/2)

REFRACTION

Refraction is a change in direction that a ray of light (or any other type of electromagnetic radiation) undergoes when it passes from a transparent medium of one density into another medium of a different density. It is one of the most basic and important phenomenon’s that affects light and is fundamental to explaining the action of lenses and prisms.When light travels from a rarer to a denser medium, it bends towards the normal and when it travels from a denser to a rarer medium, it bends away from the normal.

Although refraction usually occurs when light passes from one medium to another, there is a special case in which light does not change direction i.e. when it enters or leaves a medium at right angles to the surface.

VELOCITY AND REFRACTIVE INDEX

Light travels at different velocities in mediums of different densities. In general, the denser the medium, the slower light travels in it. The amount by which light is refracted depends on how much its velocity changes – the greater the change, the greater is the refractive power of the medium.

The absolute refractive index of a substance is a measure of the extent to which it alters the velocity. It is defined as the ratio of velocity of light in vacuum to its velocity in the medium concerned. Light rarely travels from vacuum, but usually passes between two mediums, each one of which refracts light by a different amount. In this situation, the concept of relative index is more useful. Relative index is the ratio of the velocity of light in one medium to the velocity in the other medium. It is also equal to the ratio of the absolute refractive indices of the mediums.

LAWS OF REFRACTION

There are two main laws governing refraction:

FIRST LAW:

The incident ray, the refracted ray and the normal are in the same plane. (The normal is an imaginary line drawn perpendicular to the medium’s surface at the point where the incident ray enters.)

SECOND LAW:

It is also called Snell’s Law. It states that for a given frequency of light, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media. The value of this constant is in fact equal to the relative refractive index for the mediums concerned.

Snell’s Law provides a convenient method of determining refractive indices. Such determinations can be carried out using refractometers to measure angles of incidence and refraction with great precision, and then calculating the refractive index

from these measurements. Another way of finding the refractive index involves measuring the real and apparent depths of an object immersed in a substance; the refractive index is the ratio of the real depth to the apparent depth.

REFRACTION BY PRISM

The prism, in one or another of its many forms, is second only to the lens as the most useful piece of optical apparatus.

AIM OF THE EXPERIMENT

1) To plot the graph showing the variation of the angle of deviation with angle of incidence for a liquid prism.

2) To determine the angle of minimum deviation.3) To calculate refractive index of the liquid in the prism.

APPARATUS REQUIRED

1) Drawing Board2) Sheets of white paper3) Drawing pins4) Fine pencil5) Few pins6) Half meter scale7) Protractor8) Graph sheets9) Glycerine10) Ethyl Alcohol11) Water12) Hollow Prism

FORMULA

As discussed, the refractive index of the liquid in the prism is given by prism formula:

μ = sin(A+m)/2 sin (A/2)

where A is angle of prism and is m the angle of minimum deviation.

PROCEDURE

1. Fix the white sheet of paper on the drawing board with the help of drawing pins.

2. Draw a line XX at the center of the sheets parallel to its length. Take a point L on this line.

3. Using protractor draw normal LN on the line XX.4. Place prism ABC such that its face AB lies on XX and

L is roughly at the center of AB. Mark the boundary of the prism. Draw a line KL making an angle I with LN. Plot two pins P1 and P2 vertically on KL.

5. Look for images of pins P1 and P2 from the face AC of the liquid prism keeping one of your eyes closed. Plot two more pins P3 and P4 such that these are exactly in line with the images of pins P1 and P2.

6. Remove the pins; join the pinpricks P3 and P4, which act as the emergent ray for the incident ray KL. Measure the angle of deviation suffered by the ray as shown in the following figure.

7. Conduct the experiment with angle of incidences 30,35,40,45,50 and 55, and measure angle of deviation for each.

8. Measure the angle of prism A from the marked boundary of the prism.

Liquid Used in the Prism – Water:

Serial No. Angle of incidence (i)

Angle of deviation ()

1 30 282 35 273 40 244 45 255 50 266 55 28

CALCULATION OF REFRACTIVE INDEX OF WATER:

m for water = 24o

μ = sin(A+m)/2 sin A/2 = sin (60 o + 24 o )/2 sin 30o

= sin 42 o sin30o

= 1.338

Liquid Used in the Prism – Ethanol:

Serial No. Angle of incidence (i)

Angle of deviation ()

1 30 302 35 293 40 27.54 45 255 50 266 55 28

CALCULATION OF REFRACTIVE INDEX OF ETHANOL:

m for ethanol = 25o

μ = sin(A+m)/2 sin A/2 = sin (60 o + 25 o )/2 sin 30o

= sin 42.5 o sin30o

= 1.361

Liquid Used in the Prism – Glycerine:

Serial No. Angle of Angle of

incidence (i) deviation ()1 40 39.52 45 373 50 36.54 55 35