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Let the refractive index of a denser medium with respect to a rarer medium be n₁₂ and its critical angle θ_C. At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90°. Angle A is given by

Asked in JEE Main Online 2017 · Total internal reflection and optical fibres

• (1) 1/(tan⁻¹(sin θ_C))
• (2) 1/(cos⁻¹(sin θ_C))
• (3) tan⁻¹(sin θ_C)
• (4) cos⁻¹(sin θ_C)

Step-by-step solution

Why the other options are wrong

• (1) Writes 1/(tan⁻¹) for the inverse function.
• (2) Inverts an inverse-cosine, not meaningful here.
• (4) Uses cos A=sin θ_C, the wrong trig link.

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