The exit surface of a prism with refractive index 
is coated with a material having refractive index 
. When this prism is set for minimum angle of deviation, it exactly meets the condition of critical angle. The prism angle is 
Text Solution
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Let the refractive index of the prism be 
and the refractive index of the coating on the exit surface be 
.
At the condition of minimum deviation, the angle of refraction at the first surface 
and the angle of incidence at the second surface 
are equal, i.e., 
, where 
is the prism angle.
The problem states that at the exit surface, the light meets the condition of critical angle. There fore, 
.
The critical angle 
for the interface between the prism and the coating is given by 
.
Substituting the values, 
.
Thus, 
.
Since 
, we have 
.
Using the relation 
for minimum deviation, we get 
.
Therefore, 
.
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