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For a prism of refractive index 1.732, the angle of minimum deviation is equal to the angle of the prism. Then the angle of the prism is ______.

Asked in GUJCET 2009 · Deviation and minimum deviation

Answer: (1) 60°

Step-by-step solution

Given: μ=1.732=√3 and δₘ=A.

Idea: at minimum deviation the ray passes symmetrically, and μ=(sin ((A+δₘ)/2))/(sin (A/2)).

Putting δₘ=A makes the numerator sin A:

μ=(sin A)/(sin (A/2))=(2 sin (A/2)cos (A/2))/(sin (A/2))=2 cos (A/2).

So cos (A/2)=(1.732)/2=0.866, giving A/2=30°.

The angle of the prism is A=60°.

Why the other options are wrong

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