Question

Derive the expression for refractive index of the material of the prism in terms of angle of the prism and angle of minimum deviation.

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Solution
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In the given diagram,

is the incidence ray, which is making the angle  with normal, and is the angle of emergence, which is represented by . is the prism angle and is the refractive index of the prism.

Now, We know that,

Prism angle, Angle of deviation, Angle of incidence, Angle of emergent.

In the case of minimum deviation,


SO,



Now, again

In the case of minimum deviation
 
and

So,

Now,

Now, from snell's rule,


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