Snells Law Deviation

4.
SNELLS LAW AND THE METHOD OF PATH DEVIATION
1.1. AIM
1. To determine the refractive index of a glass slide or slab using Snells law and the
method of path deviation
2. To compare the results obtained by the two methods
1.2 PRINCIPLE
The laws of reflection and transmission are widely known:
o The incident ray, the reflected ray, the transmitted ray and the normal to the
surface at the point of incidence all lie on the same plane.
o Angle of incidence (i) is equal to angle of reflection (r).
=
o The refractive index n of transmitting medium with respect to incidence medium
is given by the ratio of sine of the angle of incidence (i) to the sine of the angle
of transmission(t):
( )
=
( )
This theorem is widely known as Snells law.
Refractive index of a sample material can be calculated using Snells law directly by
measuring the angle of incidence and angle of refraction.
( )
1 =
( )
It can also be calculated by measuring the path deviation of incident ray.
2
2 = ( )( )
2 + 2 2
where l = distance that would have been travelled by incident ray in absence of medium
b= distance travelled by refracted ray
d=path deviation of incident ray
1
1.3.EQUIPMENTS REQUIRED
Sl. No. Required item Utility
1 Glass slab/slide Sample material
2 Geometry set To measure angles and lengths
3 Laser Nondispersive light source
4 A4 Sheet/ Optics Disc Set To mark and measure lengths and light rays
Sheet involved
Hook =
Spring
Hanger with
weights
Ruler
1 =
(a) (b)
Figure 1: (a) Experimental Set-up (b) Free body diagram
1.4. PROCEDURE
Two physical quantities need to be measured in this experiment Length and Angle.
Make the following table
S.No Physical Quantity Measured with Least Count

1 Length Metre Scale 1mm
2 Angle Protractor 1
A. Refractive index by Snells Law:
2
1. Place the sample (glass slab/slide) on a white A4 sheet and trace its boundary on the
sheet.
2. Align the laser to the sample and switch it on after connecting it to the power supply.
3. Trace the incident and refracted light rays.
4. Remove the sample and draw the normal to the interface at the point of incidence and
at the point where refracted ray appears out of the sample.
5. Measure the angle of incidence and angle of refraction.
6. Calculate refractive index of sample with respect to air using Snells Law.
Note : If an Optics Disc Set graded sheet is used, angles can be measured directly
B. Refractive index by the method of path deviation
1. Place the sample (glass slab/slide) on a white A4 sheet and trace its boundary on the
sheet.
2. Align the laser to the sample and switch it on after connecting it to the power supply.
3. Trace the incident and refracted light rays.
4. Remove the sample and draw the normal to the interface at the point of incidence and
at the point where refracted ray appears out of the sample.
5. Trace the path the incident ray would have taken in the absence of the sample.
6. Measure the deviation between the paths of incident ray in the presence of sample and
in absence of sample (d) using a metre scale.
7. Measure distance travelled by refracted ray (b) and the distance the incident ray would
have travelled in the absence of the sample (l).
1.5. TABLES FOR RECORDING THE DATA 1
Table 1: Angle of incidence and Angle of refraction observation table

S.No: Angle of Angle of Sin(i) Sin(r) Refractive
Incidence Refraction Index (n1)
(i) (r)
1
2
3
4
3
Table 2: Observation Table for Time Periods
S.No: Angle of Path deviation Distance Distance incident ray Sin(i) Refractive
Incidence of light ray (d) travelled by would have travelled Index (n2)
(i) refracted ray in absence of medium
(b) (l)
1
2
3
4
5
1.6 STUDY QUESTIONS

1. How would refractive index of sample vary with the color of laser used?
2. What would be the measured refractive index of sample if it was completely immersed
in a tray filled with water?
1.7 FURTHER SCOPE OF EXPERIMENTS

1. Lasers of different wavelengths can be used to determine the refractive index of sample
corresponding to those wavelengths of light. An n() vs graph can be plotted.
1.8 PRECAUTIONS
1.9 SOURCES OF ERROR
1.10 THEORY
1. Refractive index of a medium (n) is defined as the ratio of speed of light (c) in vacuum
to that in the medium (v).

=

4
2. The theory central to the experiment is the Snells law. When light is incident at the
interface to two mediums, a part of it is reflected and the rest it transmitted. Defining
the angle of incidence (i) as the angle the incident light makes with the normal to the
interface and the angle of transmission (t) as the angle the transmitted ray makes with
the normal to the interface, one finds that, for a given pair of mediums, the ratio of the
Sines of these angles is a constant. This constant is found to be the relative refractive
index between the two mediums. This theorem is known as Snells law.
( )
=
( )
1.11 FURTHER READING AND RESOURCES
Text books
Eugene Hecht (2002). Chapter 4. The Propagation of Light. In Optics, 4th Edition (4th ed, pp
117-119). Pearson Education.
Internet
Nave, C. R. (2012). Refraction of Light. Retrieved from HyperPhysics:
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/refr.html#c1
Java apps/apps
University of Colorado, B. (n.d.). Light & Radiation. Retrieved from PhET Interactive
Simulations:https://phet.colorado.edu/sims/html/bending-light/latest/bending-light_en.html
Videos
MrWaynesClass (2012, March). Snell's Law Procedure. Retrieved from
YouTube: https://www.youtube.com/watch?v=z0zF9MtF_Z4
Lewin, W. H. (1999). MIT 8.02x Physics II: Electricity and Magnetism, Fall 1999. Lecture 29:
Snell's Law, Refraction and Total Reflection. Retrieved from
Youtube: https://www.youtube.com/watch?v=8lSMnhS5eWk
Bibliography
John W. Shirley (1950) An Early Experimental Determination of Snell's Law. American
Journal of Physics.19, 507 (1951); doi: 10.1119/1.1933068
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4.

SNELLS LAW AND THE METHOD OF PATH DEVIATION

S.No Physical Quantity Measured with Least Count

A. Refractive index by Snells Law:

Table 1: Angle of incidence and Angle of refraction observation table

1.6 STUDY QUESTIONS

1.7 FURTHER SCOPE OF EXPERIMENTS

1.9 SOURCES OF ERROR

1.11 FURTHER READING AND RESOURCES

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