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

(B) Statement I is true but Statement II is false.

(A) Both Statements I and Statement II are true.

(C) Both Statement I and Statement II are false.

(D) Statement I is false but Statement II is true.

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Wave Optics

Given below are two statements :

Statement I: If the Brewster's angle for the light propagating from air to glass is

θ_{B}

, then Brewster's angle for the light propagating from glass to air is

\frac{π}{2} - θ_{B}

.
Statement II : The Brewster's angle for the light propagating from glass to air is

tan^{- 1} (μ_{g})

where

μ_{g}

is the refractive index of glass.
In the light of the above statements, choose the correct answer from the options given below :

Answer: (B)

Passing from air into glass, the Brewster angle satisfies

tan θ_{B} = μ_{g}

. For the reverse passage, glass into air, the condition becomes

tan θ_{B}^{'} = 1/ μ_{g} = cot θ_{B}

, which means

θ_{B}^{'} = \frac{π}{2} - θ_{B}

, so the first statement is correct. The second statement sets the glass-to-air angle at

tan^{- 1} (μ_{g})

, whereas it should be

tan^{- 1} (1/ μ_{g})

, so it is wrong. The first statement is true and the second is false.

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Single correct option