Question

A transparent cube of side d, made of a material of refractive index μ₂, is immersed in a liquid of refractive index μ₁(μ₁ < μ₂). A ray is incident on the face AB at an angle q(shown in the figure). Total internal reflection takes place at point E on the face BC. The q must satisfy : (A) θ > sin⁻¹(μ₁/μ₂)
(B) θ > sin⁻¹√(μ₂²/μ₁² – 1)
(C) θ < sin⁻¹(μ₁/μ₂)
(D) θ < sin⁻¹√(μ₂²/μ₁² – 1)

Answer 1

Answer:

option B...........................

Answer 2

Thus the value of angle θ = sin^-1  √μ2^2  / μ1^2

Option (D) is correct.

Explanation:

Sin c = m μ1 /  μ2

μ1 sinθ =  μ2 sin (90° - C)

Sin θ  = μ2 √  1 - μ1^2 / μ2^2 / μ1

θ = sin^-1  √μ2^2 - μ1^2 / μ1^2

θ = sin^-1  √μ2^2 /  √μ1^2

Thus the value of angle θ = sin^-1  √μ2^2 / μ1^2

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