Question

Given below are two statements :
Statement I : If the Brewster's angle for the light propagating from air to glass is $\theta_{ B }$, then the Brewster's angle for the light propagating from glass to air is $\frac{\pi}{2}-\theta_m$
Statement II : The Brewster's angle for the light propagating from glass to air is $\tan ^{-1}\left(\mu_{ g }\right)$ where $\mu_{ g }$ is the refractive index of glass
In the light of the above statements choose the correct answer from the options given below:

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Answer 1

The Correct Option is C

The problem presents two statements related to Brewster's angle and requires us to determine the truthfulness of each statement based on the given options.

Understanding Brewster's Angle:

Brewster's angle (\(\theta_B\)) is defined as the angle of incidence at which light with a certain polarization is perfectly transmitted through a transparent dielectric surface without any reflection. The formula for Brewster's angle when light travels from one medium to another is:

\(\theta_B = \tan^{-1} \left( \frac{n_2}{n_1} \right)\)

where \(n_1\) and \(n_2\) are the refractive indices of the first and second medium respectively.

Analyzing Statement I:

Statement I claims that if the Brewster's angle for light propagating from air to glass is \(\theta_B\), then the Brewster's angle for light propagating from glass to air is \(\frac{\pi}{2}-\theta_B\).

This relationship is indeed true. When calculating Brewster's angle for light going from medium 1 (air, \(n_1 \approx 1\)) to medium 2 (glass, \(n_2 = \mu_g\)), we use:

\(\theta_B = \tan^{-1} (\mu_g)\)

For light traveling from medium 2 to medium 1, the angles are complementary, i.e.,

\(\theta_B' = \frac{\pi}{2} - \theta_B\)

Since this relationship is valid, Statement I is true.

Analyzing Statement II:

Statement II claims that the Brewster's angle for light propagating from glass to air is \(\tan^{-1}(\mu_g)\), where \(\mu_g\) is the refractive index of glass.

However, this is incorrect because when light propagates from glass to air, the correct Brewster's angle is given by:

\(\theta_B' = \tan^{-1} \left( \frac{1}{\mu_g} \right)\)

Thus, Statement II is false.

Conclusion:

After analyzing both statements based on the theory of Brewster's angle and the equations involved, the correct answer is:

Statement I is true but Statement II is false