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To find the angle of incidence in order that a ray suffers minimum deviation

Solution:

As per the given criteria,

refractive index of the prism, μ=√2

Angle of the prism, A=60∘

For minimum angle of deviation we have angle of incidence is equal to angle of emergence, i.e., i=e

Hence, i=A+δm2, where δm is the minimum deviation angle.

We know,

μ=sin(A+δm2)sinA2⟹√2=sinisin602⟹sini=√2×sin(30)⟹sini=√2×12

Multiply and divide by √2, we get

sini=1√2⟹i=45∘

In order that a ray suffers minimum deviation it should be incident at an angle 45∘

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