Brewster's Law Lab Manual

Verification of Brewster's Law

Aim

To verify Brewster's law and determine the refractive index of glass using polarization of light.

Apparatus Used

Light Source
Sodium lamp or LED light source
Polarizer
Polaroid sheet or Nicol prism
Analyzer
Second polaroid sheet
Glass Plate
Plane parallel glass plate
Protractor
For angle measurement
Stand & Clamps
For mounting apparatus

Diagram

Brewster’s law

Theory

Brewster's law states that when unpolarized light is incident on a transparent surface at a particular angle called Brewster's angle (θp), the reflected light becomes completely plane polarized. At this angle, the reflected and refracted rays are perpendicular to each other.

According to Snell's law and the condition for Brewster's angle:

At Brewster's angle: \(\theta_p + \theta_r = 90°\)

Where \(\theta_r\) is the angle of refraction.

From Snell's law: \(n_1 \sin \theta_p = n_2 \sin \theta_r\)

Since \(\theta_r = 90° - \theta_p\), we have \(\sin \theta_r = \cos \theta_p\)

Therefore: \(n_1 \sin \theta_p = n_2 \cos \theta_p\)

Formula

Brewster's Law

\(\tan \theta_p = \frac{n_2}{n_1}\)

For air-glass interface (n₁ = 1):

\(n = \tan \theta_p\)

Where:

  • θₚ = Brewster's angle
  • n = Refractive index of glass
  • n₁ = Refractive index of air (≈ 1)
  • n₂ = Refractive index of glass

Procedure

Set up the light source and ensure it produces a parallel beam of unpolarized light.
Place the polarizer in front of the light source and adjust to get linearly polarized light.
Mount the glass plate on a stand that allows rotation about a horizontal axis.
Place the analyzer in the path of the reflected beam from the glass plate.
Gradually increase the angle of incidence and observe the intensity of reflected light through the analyzer.
Rotate the analyzer and note the angle at which the reflected light intensity becomes minimum (ideally zero).
Record the angle of incidence at which this occurs - this is Brewster's angle.
Repeat the experiment for different orientations and take multiple readings.
Calculate the refractive index using the formula n = tan θₚ.

Observation Table

S. No. Angle of Incidence
θₚ (degrees)		 tan θₚ Refractive Index
(n = tan θₚ)		 Remarks
1 ___ ___ ___ ___
2 ___ ___ ___ ___
3 ___ ___ ___ ___
4 ___ ___ ___ ___
5 ___ ___ ___ ___

Calculations

Mean Brewster's Angle:

\(\theta_{p,mean} = \frac{\theta_{p1} + \theta_{p2} + \theta_{p3} + \theta_{p4} + \theta_{p5}}{5}\)

Mean Refractive Index:

\(n_{mean} = \tan(\theta_{p,mean})\)

Standard Deviation:

\(\sigma = \sqrt{\frac{\sum_{i=1}^{n}(n_i - n_{mean})^2}{n-1}}\)

Percentage Error:

\(\text{Error} = \frac{|n_{observed} - n_{theoretical}|}{n_{theoretical}} \times 100\%\)

Calculation Space:

Mean Brewster's Angle = _____ degrees

Mean Refractive Index = _____

Standard Deviation = _____

Theoretical value of n for glass ≈ 1.5

Percentage Error = _____%

Result

1. Brewster's law is verified experimentally.

2. The Brewster's angle for the given glass plate = _____ degrees

3. The refractive index of glass calculated from Brewster's angle = _____

4. The percentage error in the experiment = _____%

Conclusion: The experimental results confirm Brewster's law, and the calculated refractive index is in good agreement with the theoretical value.

Precautions

Ensure the light source produces a stable and parallel beam of light.
The glass plate surface should be clean and free from scratches or dust.
Align the polarizer and analyzer carefully to avoid measurement errors.
Take readings in a darkened room to clearly observe the intensity variations.
Avoid parallax error while reading angles from the protractor.
Handle optical components carefully to prevent damage to polarizing films.
Take multiple readings and calculate the mean to reduce random errors.
Ensure the incident beam is not too intense to avoid eye strain.

Viva Voice Questions

Q1: What is Brewster's law?
Brewster's law states that when unpolarized light is incident on a transparent surface at a particular angle (Brewster's angle), the reflected light becomes completely plane polarized. At this angle, \(\tan \theta_p = \frac{n_2}{n_1}\), where n₁ and n₂ are the refractive indices of the two media.
Q2: What is the relationship between reflected and refracted rays at Brewster's angle?
At Brewster's angle, the reflected and refracted rays are perpendicular to each other, i.e., \(\theta_p + \theta_r = 90°\).
Q3: Why does the reflected light become completely polarized at Brewster's angle?
At Brewster's angle, the electric field component parallel to the plane of incidence cannot be reflected because it would have to oscillate along the direction of the reflected ray, which is impossible for transverse electromagnetic waves.
Q4: What is the typical value of Brewster's angle for glass-air interface?
For ordinary glass (n ≈ 1.5) and air interface, Brewster's angle is approximately 56.3°, since \(\tan^{-1}(1.5) = 56.3°\).
Q5: How is Brewster's law used in practical applications?
Brewster's law is used in polarizing sunglasses, camera filters, laser optics, LCD displays, and in determining refractive indices of transparent materials.
Q6: What happens if the angle of incidence is not equal to Brewster's angle?
If the angle of incidence is not equal to Brewster's angle, the reflected light will be partially polarized rather than completely polarized.
Q7: Derive the formula for Brewster's angle.
From Snell's law: \(n_1 \sin \theta_p = n_2 \sin \theta_r\). At Brewster's angle: \(\theta_p + \theta_r = 90°\), so \(\theta_r = 90° - \theta_p\). Therefore: \(\sin \theta_r = \cos \theta_p\). Substituting: \(n_1 \sin \theta_p = n_2 \cos \theta_p\), which gives \(\tan \theta_p = \frac{n_2}{n_1}\).
Q8: What is the polarization of transmitted light at Brewster's angle?
The transmitted (refracted) light at Brewster's angle is partially polarized, with the electric field component perpendicular to the plane of incidence being stronger than the parallel component.

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