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The refractive index of the material of a prism is 1.5. If δₘ=A, what is the value of the angle of the given prism? (where δₘ is the angle of minimum deviation and A is the angle of the prism)

Asked in GUJCET 2011 · Deviation and minimum deviation

Answer: (1) 82.8°

Step-by-step solution

Given: μ=1.5, and the minimum deviation equals the prism angle, δₘ=A.

Idea: at minimum deviation μ=(sin ((A+δₘ)/2))/(sin (A/2)).

With δₘ=A this collapses to μ=2 cos (A/2), because sin A=2 sin (A/2)cos (A/2).

So cos (A/2)=(1.5)/2=0.75.

A/2=cos⁻¹(0.75)=41.4°.

Doubling, the angle of the prism is A=82.8°.

Why the other options are wrong

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