Introduction
The ratio of light velocity in a medium with respect to velocity of light in air is known as refractive index of the medium. The refractive index of a medium is a measure for how much the speed of light is reduced inside the medium. For example, in a typical glass having refractive index of 1.5 means that in the glass light travels at 1 / 1.5 = 0.67 times the speed of light in the vacuum.
Refractive index is one of the most important parameters in optics. It is determined by measuring the angle of incidence and angle of refraction of a ray of light incident upon a medium; the ratio of sines of the two angles gives the refractive index. Refractive indices of glass and other transparent solid material are determined by making prisms out of them. Refractive index of a liquid is determined using a hollow prism or hollow glass slab as its container. The liquid is filled in the container and refraction of light through it is observed.
Refractive index of liquids varies from 1.33 (water) to 1.67(Mercury). This narrow range in the values of refractive index indicates that the variation in the velocity of light through liquids is small. In this experiment a rectangular glass tank is used as a container for the liquid and diffracted light coming out of the grating is made incident on the liquid which gets refracted resulting in shifting of the entire diffraction pattern from its position. This shift is measured by tracing the diffraction spots.
Refraction of Light
When a ray of light passes from one medium into another, the ray undergoes change in direction at the surface of separation of the two media. This is called refraction of light.
angle at which light falls onto the surface of the material with respect to the normal to the surface is called angle of incidence (φ). The ray bends at the boundary of the two surfaces. The angle formed between the normal to surface and refracted ray is called angle of refraction (φ´) The ratio of sines of these two angles gives the value of refraction index of the material.
Similar to visible light, a laser light also gets refracted by a medium. The laser rays trace its path through the transparent medium hence it is very easy to see the process of refraction as shown in Figure-1.
To increase the visibility and to make measurement accurate a low LPI (Lines per inch) grating is used. The laser light falling on the grating produces diffraction pattern as shown Figure-3, which contains series of diffraction images or spots of different order.
Figure-1: Laser light falling on the grating and emerging through the glass tank containing water (see the bending of light the at the interface of the two surfaces)
First order diffraction spot
d s Shift in the Diffraction spot due to the
material X1
Laser
Grating
Glass tank containing liquid
Central bright spot
(direct ray)
t=thickness
Screen
f
Figure-2: Process of refraction of light by a transparent material
To produce such a series of spots a low LPI (100,200,or 500LPI) grating is used. Introducing the material, whose refractive index is to be determined, is placed in between the screen and
grating. The diffracted light coming out of grating passes through the material resulting in the shift of the entire diffraction pattern.
Figure-3: Diffraction pattern of laser light
The shift, ds, in the diffraction pattern from its original position due to refraction taking place through a medium of thickness ‘t’ is given by [1]
n cos φ
d s = t sin φ1 − 1
n cos
…1
φ′
t is thickness of the medium placed in the path of diffracted light.
φ is angle of incidence
‘
φ is the angle of refraction
n is the refractive index of the first medium (air)
n’ is the refractive index of the second medium
The laser light which is highly parallel rays of light falls normally onto the grating hence the angles ‘ φ ’ and ‘ φ′ ’are very small, of the order of fraction of a degree. Hence cos φ /cos φ ‘ is
≅ 1. Hence equation 1 reduces to
| s φ |
d = t sin 1 −
n
…2
n ′
n ′ = n t sin φ …3
t sin φ − d s
‘n’ is refraction index of air (=1). Further, the angle of refraction as seen from Figure-2
φ = 90 − θm
Where ‘θm ‘is the mth order diffraction angle of the spot.
∴ sin φ = sin(90 − θm ) = cos θm …4
Therefore the refractive index
n ′ = 1xt cos θ m …5 t cos θm − d s
For the first order diffraction spot θm=θ1
n ′ = 1xt cos θ1 …6 t cos θ1 − d s
‘θ1 ‘and ‘ds ‘ can be determined experimentally hence ‘n’ can be calculated using equation-6.
The Diffraction Angle θm
θm is the angle diffraction for the mth order spot in the diffraction pattern. For the first order spot [2]
θm = θ1 …7 is the angle formed by
tanθ1 =
x 1 …8 f
Where ‘x1 ‘ is distance between first order spot from centre spot.
‘f’ is the distance between grating and the screen
Hence
| x1 |
θ1= tan-1 …9 f
‘x1’ and ‘f’ can determined experimentally by tracing the diffraction pattern.
Apparatus Used
The apparatus consists of a diode laser 625nm red, a rectangular glass tank with 50mm x
65mm inner spacing, grating with 200LPI and a white screen. The complete experimental set- up is shown in Figure-4.
Experimental Procedure
- The Laser is set up and grating is placed in front of it so that the laser beam falls on the grating lines. The diffraction pattern is observed on a white screen placed in front of laser about 1.5m away in line with laser light.
The position of the screen should not be changed during the experiment.
Figure-4: Experimental set-up for determining refractive index
- The distance between the grating and the screen is determined using a measuring scale
f=1.5m
- The number of lines of the grating is also noted from grating
N=200LPI
The diffraction pattern on the screen is traced using a white sheet of paper and sketch pen as shown in Figure-5.
Figure-5: Diffraction pattern trace for water
The distance 2×1 is noted from the sketch.
2x117mm or x1= 8.5mm, = 8.5X10-3m
First order diffraction angle is calculated.
θ1= tan-1
x 1
f
= tan-1
8.5 × 10 −3
1.5
= tan −1
5.66×10 −3
= 0.324°
- Now glass tank containing water is placed in front of the grating as shown in Figure-4 at a distance of about 5cm from the grating. The shift in the position of the diffraction pattern is also noted as shown in the Figure-5.
The shift in the diffraction pattern is noted ds = 6.5mm=6.5 X10-3m
The thickness of the glass tank containing water is measured using vernier calipers. t = 5cm = 50mm X10-3m
- Refractive index is calculated using equation 6.
| −3 |
n′ = 1xt cos θ1 = 1x50×10 cos 0.324 = 0.04999 = 1.149
t cos θ1
− ds
50×10− 3 cos 0.324 − 6.5×10−3
0.043499
|
Table–1
Standard values are at 200C, ** Limca is three times diluted with water
- The experiment is repeated by placing the tank with its length side facing the laser beam and the shift in the diffraction pattern is noted in Table-1.
1xt cos θ 1x65x10 −3 cos 0.324 0.06499
n′ = 1 = = = 1.18
t cos θ1
− ds
65×10− 3 cos 0.324 − 10×10−3
0.0549
- The experiment is repeated for acetone and other liquids listed in Table-1. In each case the diffraction pattern is noted for both the sides of the glass tank containing the liquid facing the diffracted laser light.
Results
The results obtained are tabulated in Table-2.
Table-2
| Liquid | Refractive Index | |
| Experiment | Standard* | |
| Water | 1.19 | 1.33 |
| Liquid Paraffin | 1.40 | 1.4 |
| Acetone | 1.24 | 1.6 |
| Cooking Oil | 1.15 | – |
| Diluted Limca** | 1.24 | – |
Experimental results
* Standard values are at 200C, ** Limca is 1/3 diluted with water
Discussion
- The equation in the simplified form (give equation -6) appears more accurate because the angle of diffraction is small.
- Displacement of the diffraction pattern does not depend on grating LPI. Hence the experiment can be performed with any grating. However, large LPI grating (15000 or
25000 LPI) will produce large separation different order spots. Hence one would need a wider screen to display the diffraction pattern.
- Since laser light produces highly parallel beam of rays, in the equation for refractive index the value of the “cosθ” term is unity for all the cases. Hence one need not calculate cosθ while calculating refractive index and the formula for refractive index of liquid becomes
n ′ = nt
t − d s
References
[1] F A Jenkins and H E White, Fundamentals of Optics Page-29, McGraw-Hill Book
Company
[2] Jeethendra Kumar P K, Diffraction Grating, Lab Experiments Vol-6, No-1, Page-22
