Download Polarization of light II

Lecture 2
Polarization of light II
Objective:
To study the polarization of light via reflection and to measure the Brewster angle.
Theory:
When an electromagnetic wave is incident upon the interface of two dielectric media then
part of that wave is reflected and remaining part is transmitted as shown in Fig 1
(incorporate fig 1 of module 13, lecture 2). The magnitude of reflected and the
transmitted wave for s and p polarization are governed by Fresnel’s equations. Fresnel’s
equations for reflected electric field are given by,
 n cos  I  n 2 cos  T
E Rs   1
 n1 cos  I  n 2 cos  T
 s
 E I

(1)
 n cos  T  n 2 cos  I
E Rp   1
 n1 cos  T  n 2 cos  I
 p
 E I

(2)
E Is , E Ip , E Rs and E Rp are the magnitudes of incident and reflected electric fields for s and
p polarisation respectively,  I and  T are the incidence and transmitted angles and n1
and n 2 are the refractive indices of two medium. The reflected intensity for both the
polarization is given by:
2
 n cos  I  n2 cos T  s
I  1
 II
 n1 cos  I  n2 cos T 
s
R
(3)
2
 n cos T  n2 cos  I  p
I  1
 II
 n1 cos T  n2 cos  I 
p
R
(4)
Thus the reflectivity for both the polarisation depends on the refractive index and angle of
incidence. Reflectivity for p polarisation (eqn.2) goes to zero at certain angle of incidence
called Brewster angle (  B ) given by
tan  B  n2 n1
.
(5)
This fact can be used to get a polarised beam of light from an unpolarised beam. An
unpolarised beam is made to incident at an interface at Brewster angle. The reflected
beam will contain the s component only. In this experiment , you will study the variation
of intensity as a function of angle of incidence for p as well s polarized light and will
measure the Brewster angle for air and glass interface and hence refractive index for glass
can be estimated from eq (5).
Procedure:
The experiment set-up consists of a diode laser, a glass plate, polarizer, a photodiode
and digital multimeter or micro ammeter. The polarizer is fitted with a circular scale to
record the angular orientation in the plane normal to the incident light. Photodiode is
used to measure the intensity of light. All the components can be mounted on an
optical bench for proper alignment as given below.
h
A/DMM
Fig 2: Photodiode circuit (this circuit can be
transferred from Module 17, lecture 4, fig 2)
1. Place the glass slab on a rotational table table horizontally as shown in fig 3
(transfer fig 3. from Module 17, lecture 4, fig 2). Alternatively it can be placed
on a trotractor. and align it with the laser beam for normal incidence. The normal
incidence can be ensured by tracing the reflected beam back to the source. Then
rotate the glass plate by five degree or so so that you can see the reflected light
clearly.
2. Arrange the photodiode behind the analyzer to stect the intensity of the light
passing through it.
3. Record the intensity of reflected beam for both the components (s and p
components) separately (analyzer is to be set accordingly) as a function of angle
of incidence whch can be changed by rotating the glass plate as shown in the fig
3.
Analyses of data:
1. Plot the intensity for both s and p components as a function of angle of incidence
as shown in fig 4..
2. Veryfy from the plot that it follows eq 3 and 4.
3. Note down the angle at which intensity is zero for s component. This angle is the
Brewsetr angle.
4. From eq 5 estimate the refractive index of glass.