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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 θ (shown in the figure). Total internal reflection takes place at point E on the face BC. The θ must satisfy:

θ<sin⁻¹;μ₂²/μ₁²-1;

θ>sin⁻¹;μ₂²/μ₁²-1;

θ>sin⁻¹;μ₁/μ₂

θ<sin⁻¹;μ₁/μ₂

Solution:

Correct option is B. θ<sin⁻¹;μ₂²/μ₁²-1;sin c=μ₁/μ₂μ₁sin θ=μ₂sin(90⁰-C)sin θ=μ₂√(1-μ₁²/μ₂²)μ₁θ=sin⁻¹;μ₂²/μ₁²-1;For TIR θ>sin⁻¹;μ₂²/μ₁²-1;