This document describes an experiment to study Brewster's angle and polarization of light by reflection. Brewster's angle is defined as the angle of incidence at which light with a particular polarization is perfectly transmitted through a boundary between two transparent materials, without any reflection. The experimental setup involves a laser, polarizer, photodetector, glass plate, and rotational mount. By measuring the intensity of reflected light at different angles of incidence, Brewster's angle for the glass-air interface can be determined as the angle with minimal reflection. Applications of Brewster's angle discussed include polarized sunglasses, camera lenses, windows, and microscopy.

1. BREWSTER’S ANGLE

2. AIM
To study the polarization of light by simple reflection that is to study
Brewster's law.

3. APPARATUS REQUIRED
• He laser
• Dial fitted polarizer
• Photo detector
• Micro ammeter
• Rotational mount
• Glass plate
• Constant power supply

4. THEORY BEHIND THE EXPERIMENT
• When light moves between two media of differing refractive index (n), some of the
light is reflected from the surface of the denser material. This reflected ray’s intensity
changes with change in the incident angle (𝜃𝐵) at the interface of two mediums. At one
specific angle of incidence of light only perpendicular vibrations of electric field vectors
are reflected whereas parallel vibrations are restricted or polarized. This loss in light
intensity is due to polarization by reflection and the angle of incidence for which
reflected ray is polarized is called the Brewster's angle θ B (also known as the
Polarization angle).
• The fraction of the incident light that is reflected depends on both the angle of
incidence and the polarization direction of the incident light. The functions that
describe the reflection of light polarized parallel and perpendicular to the plane of
incidence are called the Fresnel Equations. According to the Fresnel Law when light
moves from a medium of a given refractive index (𝑛1) into a second medium with
refractive index (𝑛2), both reflection and refraction of the light may occur.

5. DEFINITION OF BREWSTER'S ANGLE
• The angle of incidence at which light with a particular polarization is perfectly
transmitted, without any reflection.
• When unpolarized light is incident at this angle, the reflected signal would be perfectly
polarized:

6. DERIVATION OF BREWSTER'S ANGLE
• At Brewster's Angle, the reflected and transmitted waves must be orthogonal
• To find Brewster's Angle, solve for θ in the following equations:
θ = 90˚ - θ1
θ1 + θ2 = 180˚ - 90˚ = 90˚
θ1 = θ1
𝑛1*sin(θ1) = 𝑛2*sin(θ2)
θ =tan−1 (𝑛1/𝑛2)

7. FRESNEL EQUATIONS & BREWSTER'S LAW
• The portion of a wave reflected when it encounters a boundary between two media is
described by the Fresnel equations
• The Fresnel equations predict that light with p polarization will not be reflected if the
angle of incidence is tan 𝜃𝐵 =
𝑛𝑡
𝑛𝑖
where 𝑛𝑡 and 𝑛𝑖 are the indices of refraction of the
media
• This relationship is known as Brewster's Law

8. FRESNEL EQUATIONS & BREWSTER'S
LAW

9. EXPERIMENTAL SETUP

10. PROCEDURE
• Set up the system shown In figure. Be sure the glass reflecting material is vertical and centered
over the axis of rotation of the rotational stage. Glass reflecting material was setup such that at
90° on the protractor, the incident ray (from a red He Laser source) hit the surface
perpendicularly so the reflected beam goes back into the laser aperture. Be sure that the
rotational stage reads 0o at this point.
• Darken the room as much as possible.
• Adjust the laser so the output is horizontally polarized.
• The protractor is then rotated to angle values less than 90° in an interval of 5o . The reflected ray
is directed to a fiber optic light intensity sensor which measures the intensity of the reflected
light in terms of current. Record the current in micro ammeter . This alignment of the incoming
laser and the protractor ensures that the angle on the protractor equals the angle of the incident
ray, thus gives the value of the incidence angle. The angle range is limited between 20° and 80°
because of the expanse of the fiber optic light intensity sensor holder.
• Between the angles of 50o and 60o , measure the intensity of reflected beam in 2o increment.
You will notice that at a certain angle, Brewster’s angle, there will be little or no reflected light.
Record this angle.

11. OBSERVATIONS

12. DATA ANALYSIS
• Applying Brewster's Law, we can now determine the index of refraction of the styrene
pellets
• Since it is known that: tan 𝜃𝐵 =
𝑛2
𝑛1
𝑛2= 𝑛1 tan 𝜃𝐵
𝑛2 ≈ tan 56˚ ≈ 1.4
• From the graph, Brewster's angle is Ѳ= 56°. We can conclude that if an un polarized
light is incident at angle is equal to 56° then Reflected light will be plane polarized
where reflected light does not contain E-vector parallel components , it contains only
perpendicular components . We can tell that polarization involved in this experiment.
Through digital meter set up we can easily find an Brewster's angle compared to
spectrometer & very less time consuming.

13. PLOT OF POWER (CURRENT I) VS
ANGLE ‘𝜽’

14. PRECAUTION
• The laser beam should not penetrate into eyes as this may damage the eyes
permanently.
• The photo detector should be as away from the slit as possible.
• The laser should be operated at a constant voltage 220V obtained from a stabilizer.
This avoids the flickering of the laser beam.
• Laser should be started at least 15 minutes before starting the experiment.
• Scale of Vernier should be rotated slowly.
• Room should be perfectly dark.

15. APPLICATION: POLAROID
SUNGLASSES
• Glare consists almost entirely of horizontally polarized light.
• Vertically polarized light is useful for human vision.
• Polarized sunglasses can selectively block certain polarizations of light.

16. APPLICATION: POLARIZED CAMERA
LENSES
Unpolarized Polarized

17. APPLICATION: BREWSTER WINDOWS
• Whenever a wave passes through a transparent window, some degree of optical loss
will occur.
• Even with an anti-reflective coating, a normal glass pane will have a reflectivity of
around 0.2% on each side.
• Brewster windows are tilted to create an angle of incidence close to Brewster's angle.
• Result in at least 10 times lower losses.

18. APPLICATION: BREWSTER ANGLE
MICROSCOPY
• Used to detect changes in refractive index on water surface.
• Water surface does not reflect light, appears black.
• When surfactants alter the refractive index, Brewster's Angle changes locally and a
reflected wave is observable

19. DEMONSTRATIONS
• Mathematica plot of absorbed/reflected light
https://demonstrations.wolfram.com/FresnelEquations/
• Visual of polarized light hitting a medium at Brewster's Angle
https://vlab.amrita.edu/index.php?sub=1&brch=189&sim=333&cnt=4

20. REFRENCES
• http://en.wikipedia.org/wiki/Brewsters_angle
• https://vlab.amrita.edu/?sub=1&brch=189&sim=333&cnt=2
• https://www.iitr.ac.in/departments/PH/uploads/Teaching%20Laboratory/12%20Brewste
rs%20angle.pdf