Thermal Radiation
Experiment 2: Brewster’s Angle
Written Report
Submitted by:
方查斯
林承翰
林哲偉
蔡育安
Submitted to:
Prof. Yueh-Heng Li
Department of Aeronautics and Astronautics
National Cheng Kung University
May 8, 2023
Introduction
Light and all other electromagnetic (EM) wave sources propagating toward a
certain interface must either be reflected, absorbed, or transmitted. A medium is
considered a dielectric if it does not absorb incident radiation. When a beam of EM
wave travels to this medium and encounters an interface of another dielectric
medium, some of the wave is refracted into the second medium while the rest is
reflected. Snell’s law proves that the angle of incidence should be the same as the
angle of reflection and is the concept behind the mirror-like or specular reflective
properties.
Incident radiation has two associated components – the electric and magnetic
fields that oscillate with respect to the direction of propagation. Both fields are also
perpendicular from each other, and the total intensity can be taken as the sum of
these two components. Incident light can be polarized in any plane, but a traditional
nomenclature of parallel and perpendicular components is mostly adopted. The
specular reflectivity of the incident wave on an interface will also result in polarized
parallel or perpendicular relative to the plane of incidence. For convenience, some of
the properties such as the refractive index, electric permittivity, and dielectric constant
of the mediums of interest are assumed not to have any angular dependence.
A notable scenario is when incident radiation is transmitted through a dielectric
surface and the reflected light becomes completely polarized or propagating in only
one fixed plane. This angle of incidence is called the Brewster angle, and it is a
function of the refractive index as well as the incident and refraction angles. In
experiments, Brewster angle can be determined by inspection of the incident light
passing through a polarizer to a surface, and then measuring the intensity of light
reflected. A schematic of a laser-plate-detector system to observe the occurrence of
Brewster angle is illustrated in Fig 1.
Fig 1. Schematic of laser-plate-detector system
The objectives of the experiment are as follows: 1.) To determine the Brewster’s
angle based on experimental data, and 2.) To compare the experimental and
theoretical outcomes in determining Brewster’s angle
Laser is unpolarized at initial but when it incident on triangular prism the laser
become to polarized and it is divided into refracted and reflected light.
The perpendicular polarized is more than parallel polarized in reflected light and
( )
( )
𝑛2
when the incident angle θ𝑖 =
𝑛1
the reflected light will only exist polarized light
( )
perpendicular to incident.where the θ𝑖 is defined as Brewster's angle.
The parameters is defined follow:
n:reflectivity
θ𝑖 =
( )
𝑛2
𝑛1
⎧
⎪
2
( )
( ) ⎨
⎪( )
⎩
ρ‖ θ𝑖 =
𝑛2
𝑛1
𝑛2
𝑛1
2
2
⎤
−θ𝑖 ⎥
⎥
⎦
2
⎤
−θ𝑖 ⎥
⎥
⎦
( )
( )
⎡
cos𝑐𝑜𝑠 θ𝑖 −⎢
⎢
⎣
𝑛2
⎡
cos𝑐𝑜𝑠 θ𝑖 +⎢
⎢
⎣
𝑛2
𝑛1
𝑛1
1
2
1
2
2
⎫
⎪
⎬
⎪
⎭
⎧⎡
⎪ ⎢⎢
2
1
2
2
1
2
( )
( ) ⎨
⎪ ( )
⎩
ρ⊥ θ𝑖 =
⎣
⎡
⎢
⎢
⎣
𝑛2
𝑛1
𝑛2
𝑛1
2
⎤
−θ𝑖 ⎥ −cos𝑐𝑜𝑠 θ𝑖
⎥
⎦
⎤
−θ𝑖 ⎥ +cos𝑐𝑜𝑠 θ𝑖
⎥
⎦
⎫
⎪
⎬
⎪
⎭
Materials and Methods
The experiment uses a system consisting of a laser light source, Brewster
plate, polarizer, black receiving panel, and polarizer. The plate and polarizer
orientation were rotated in small angular increments relative to the incident light
source. The detector used for the reflected radiation is the integrating sphere
connected to a computer and gives the reflectivity in terms of intensity
Fig 2. Experimental setup
( )
ρ‖ θ𝑖 =
⎧
⎪
2
( )
⎨
⎪( )
⎩
𝑛2
𝑛1
𝑛2
𝑛1
2
2
⎤
−θ𝑖 ⎥
⎥
⎦
2
⎤
−θ𝑖 ⎥
⎥
⎦
( )
( )
⎡
cos𝑐𝑜𝑠 θ𝑖 −⎢
⎢
⎣
𝑛2
⎡
cos𝑐𝑜𝑠 θ𝑖 +⎢
⎢
⎣
𝑛2
𝑛1
𝑛1
1
2
1
2
2
⎫
⎪
⎬
⎪
⎭
(1)
⎧⎡
⎪ ⎢⎢
2
1
2
2
1
2
( )
( ) ⎨
⎪ ( )
⎩
ρ⊥ θ𝑖 =
( )
⎣
⎡
⎢
⎢
⎣
𝑛2
𝑛1
𝑛2
𝑛1
2
⎤
−θ𝑖 ⎥ −cos𝑐𝑜𝑠 θ𝑖
⎥
⎦
⎤
−θ𝑖 ⎥ +cos𝑐𝑜𝑠 θ𝑖
⎥
⎦
where ρ‖ θ𝑖 = 0 when θ𝑖 =
( )
𝑛2
𝑛1
⎫
⎪
(2)
⎬
⎪
⎭
. At this point, θ𝑖 is called the Brewster’s angle as
radiation reflected from energy incident at this angle is all perpendicularly polarized.
Fig 3. Experimental flowchart
We use the property of Brewster's angle that incident angleθ =
𝑖
( )
ρ‖ θ𝑖 = 0.
( )
𝑛2
𝑛1
the
First we use integral sphere to measure the energy of environment after that we incident the
laser to the triangular prism and use the polarizer so the reflexive laser receive the by
the integral sphere is only the paralleled polarized laser.
So by the integral sphere we can measure the energy and find which one is equal the
environment the angle of the incident is Brewster's angle.
Results and Discussion
Table 1 lists the recorded data based on the recorded total intensity received
by the integrating sphere instrument positioned according to the direction of reflected
light. With this, the data can be treated as the recorded reflective intensity. To reduce
the noise from the environment, a baseline data was recorded and then subtracted to
the acquired data in the actual experimental runs.
Table 1. Recorded reflective intensity data and corresponding theoretical reflective intensity
Incident Angle Net Reflective Intensity*
θ𝑖, deg
10
20
30
40
45
50
55
60
70
80
640
540
440
240
130
40
0
190
1240
19440
*Taken with a background environment intensity of 560
To observe the energy of reflexive laser can find the intensity of 55 degree is equal
the environment intensity so Brewster's angle is 55 degree.
Fig 4. Experimental and theoretical reflective intensity
In Fig 4, The experimental data is overlayed against the theoretical reflectivity
for a considerable range of incident angles.
Fig 5. Illustration of two reflection spots
– Why do two reflection spots appear, and which one is correct?
The right one is correct, due to the reflective and refractive phenomenon on the prism
, refractive one was causing due to the penetrate on the prism directly,reflective one
also begin the refraction at the first time but the light also hit on the another surface
of the prism, resulting it reflect on its surface,causing the second one spots.
– potential sources of error:
The human error can be divided by two parts, first one is the uncertainty value of
incident light through into the integrating sphere, in experimental process, the
observer should hold on the integrating sphere on hand and follow the light on
different angle, resulting in the value of intensity of incident light become very
variantly due to the light can’t hit on the integrating sphere uniformly.
As for the error due to the detector capability can attribute to exaggerated random
value detected by integrating sphere, the value can’t be catched on a definite one
,causing the huge uncertainty on the experimental results compared to theoretical
value.
References Cited
Introduction of Brewster's angle
https://zh.wikipedia.org/zh-tw/%E5%B8%83%E5%84%92%E6%96%AF%E7%89%B
9%E8%A7%92
Introduction of polarization
https://zh.wikipedia.org/zh-tw/%E5%81%8F%E6%8C%AF