S-108-2110 OPTICS
Labwork: Reflection and Refraction
1/6
REFLECTION AND REFRACTION
Student Labwork
S-108-2110 OPTICS
Labwork: Reflection and Refraction
Table of contents
1. Theory......................................................................................................................................3
2. Performing the measurements..................................................................................................4
2.1. Total internal reflection....................................................................................................4
2.2. Brewster angle..................................................................................................................5
3. Measurement report..................................................................................................................6
2/6
S-108-2110 OPTICS
Labwork: Reflection and Refraction
3/6
1 Theory
In this work we study the total internal reflection and Brwester angle using polarized light. A laser source,
polarizer, rotation stage and D–shaped acrylic plate will be used to carry out the measurements and
determine the index of refraction of the acrylic plate.
The measurement setup for total internal reflection is depicted in Figure 1. Due to the D-shaped form of the
plate, the beam path from air to acrylic will not change.
n2
n1
Acrylic plate
Figure1. Measuring the total internal reflection.
First we determine the angle θc where the total internal reflection occurs. This presupposes, that
n1>n2.
Snell’s law (also known as law of refraction) tells that
n1 sin θ1 = n2 sin θ2.
The angle of total internal reflection can be calculated when taking
θ2 = 90  θ1= θc.

The relative index of refraction for the acrylic plate becomes then
The Brewster angle will be determined using similar setup but the measurements will be carried out using
both propagation directions, i.e. beam going from air to acrylic (n1 < n2) and from acrylic to air (n1 > n2).
First the incident light has to be polarized in the plane of incidence. In this case the intensity of the reflected
beam will be zero if the angle of incidence satisfies the condition
or using markings in the lecture notes
.
Angle θP is called the polarization angle or Brewster angle. When light is incident under Brewster angle the
following relation is valid
θ1 + θ2 = 90 .
S-108-2110 OPTICS
Labwork: Reflection and Refraction
4/6
In the following we’ll use two different setups regarding beam propagation direction: n1< n2 (n1 = air, n2 =
acrylic) and n1> n2 (n1= acrylic, n2= air)
1) n1=air, n2=acrylic:
The experimental setup is shown in figure 2. In this case we’ll get
tan θp =n
Acrylic plate
Figure 2. Brewster angle in case of n1 < n2.
2) n1=acrylic, n2=air:
The experimental setup is shown in figure 3. Accordingly we’ll get
Acrylic plate
Figure 3. Brewster angle in case of n1 > n2.
2.
Performing the measurements
2.1 Total internal reflection
First set the acrylic plate with the round surface facing the light source. Then set the angle of incidence from
the plane surface to be zero (θ1= 0). This is easiest to achieve observing the back-reflected beam from the
plane surface of the plate. If the beam reflects back to the source then the plane surface is perpendicular with
the incoming beam. Mark the corresponding angle on the rotation stage as α0. Thereafter find the two angles
α1 and α2 at which the total internal reflection occurs. This holds true when the reflected beam propagates
along the plane surface. Experimental setup is shown in figure 4.
S-108-2110 OPTICS
Labwork: Reflection and Refraction
5/6
Figure 4. Measuring the total internal reflection.
The angle of total internal reflection can be determined from the following relation.
|
|
To calculate θc one does not need actually find α0. This is only used to verify the measurement correctness. In
the measurement report find the quantities |α1 – α0| and |α0 – α2|. If measurement is correctly performed these
quantities have to be equal within the measurement uncertainty.
2.2 Brewster angle
In the case of n1 < n2 (n1 = air, n2 = acrylic) align the back-reflected beam from plane surface to coincide
with the incoming beam. The angle of incidence is then zero. Mark the corresponding angle β0 in the rotation
stage. Using the polarizer set the light to be linearly polarized in the plane of incidence. Polarizing plane is
marked on the polarizer. Then find the two angles β1 and β2 at which the back-reflected beam disappears.
Polarization angle θP can be found as
|
|
In the case of n1> n2 (n1= acrylic, n2= air) carry on similar way but mark the angles as γ0, γ1 and γ2.
S-108-2110 OPTICS
Labwork: Reflection and Refraction
6/6
Measurement report
Name and student number:
c = angle of total internal reflection
P = polarization angle, also known as Brewster angle
n = index of refraction
Total internal reflection:
0
1
Correctness check:
10|
20|
Brewster angle:
Propagation direction: air  acrylic glass
0
1
Correctness check:
10|
20|
Propagation direction: acrylic glass air
0
1
Correctness check:
10|
20|
2
angle of total internal reflection
c
n
Brewster angle
2
P
n
Brewster angle
2
P
n