Given below are two statements :
Statement I : If the Brewster's angle for the light propagating from air to glass is , then the Brewster's angle for the light propagating from glass to air is
Statement II : The Brewster's angle for the light propagating from glass to air is where is the refractive index of glass.
In the light of the above statements, choose the correct answer from the options given below:
Statement I : If the Brewster's angle for the light propagating from air to glass is , then the Brewster's angle for the light propagating from glass to air is
Statement II : The Brewster's angle for the light propagating from glass to air is where is the refractive index of glass.
In the light of the above statements, choose the correct answer from the options given below:
- A.Statement I is true but Statement II is false
- B.Both Statement I and Statement II are false
- C.Both Statement I and Statement II are true
- D.Statement I is false but Statement II is true
Show answer and solution
Correct option: A
Solution
For air-to-glass: tan(θ_B) = μ_g, so θ_B = tan⁻¹(μ_g).
For glass-to-air: the Brewster's angle θ_B' satisfies tan(θ_B') = 1/μ_g (since refractive index of air relative to glass is 1/μ_g).
Now, tan(π/2 - θ_B) = cot(θ_B) = 1/tan(θ_B) = 1/μ_g, which equals tan(θ_B'). So Statement I is correct.
Statement II claims the Brewster's angle from glass to air is tan⁻¹(μ_g), but it should be tan⁻¹(1/μ_g). Since μ_g > 1, tan⁻¹(μ_g) ≠ tan⁻¹(1/μ_g), so Statement II is false.
For glass-to-air: the Brewster's angle θ_B' satisfies tan(θ_B') = 1/μ_g (since refractive index of air relative to glass is 1/μ_g).
Now, tan(π/2 - θ_B) = cot(θ_B) = 1/tan(θ_B) = 1/μ_g, which equals tan(θ_B'). So Statement I is correct.
Statement II claims the Brewster's angle from glass to air is tan⁻¹(μ_g), but it should be tan⁻¹(1/μ_g). Since μ_g > 1, tan⁻¹(μ_g) ≠ tan⁻¹(1/μ_g), so Statement II is false.
[JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)]