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A glass prism having refractive index μ is placed in air. For it the angle of minimum deviation of the prism is the same as the angle of the prism. Then what is the value of the angle of the prism?

Asked in GUJCET 2021 · Deviation and minimum deviation

• (1) 2 cos⁻¹(μ/2)
• (2) 2 cos⁻¹(μ)
• (3) cos⁻¹(μ/2)
• (4) cos⁻¹(μ)

Step-by-step solution

Why the other options are wrong

• (2) The factor 2 inside the cosine has been dropped. The identity sin A=2 sin (A/2)cos (A/2) leaves cos (A/2)=μ/2, not μ — and for glass with μ=1.5 this expression does not even exist.
• (3) This is A/2, not A. The relation fixes the half-angle, so the inverse cosine must be doubled.
• (4) Both slips together: the 2 inside the cosine dropped and the half-angle left undoubled. cos⁻¹(μ) is undefined for any μ>1.

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