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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=2A+δ_{m} $, where $δ_{m}$ is the minimum deviation angle.

We know,

$μ=sin2A sin(2A+δ_{m} ) ⟹2 =sin260 sini ⟹sini=2 ×sin(30)⟹sini=2 ×21 $

Multiply and divide by $2 $, we get

$sini=2 1 ⟹i=45_{∘}$

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

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