Q.A prism of refracting angle 60° has a refractive index 1·5 in air. Calculate the angle of minimum deviation of the prism, when it is kept in a medium of refractive index 3√2/4.

The prism's effective refractive index in the medium is n(rel) = 1.5 / (3√2/4) = √2; using the prism formula with A = 60° gives an angle of minimum deviation Dm = 30°.

Given: refracting angle A = 60°, refractive index of prism in air = 1.5, refractive index of surrounding medium = 3√2/4.

Step 1 - Relative refractive index (prism with respect to the medium):

n(rel) = 1.5 / (3√2/4) = 1.5 x 4 / (3√2) = 6 / (3√2) = 2/√2 = √2.

Step 2 - Prism formula at minimum deviation:

n(rel) = sin((A + Dm)/2) / sin(A/2).

sin(A/2) = sin30° = 1/2.

So sin((A + Dm)/2) = n(rel) x sin(A/2) = √2 x 1/2 = 1/√2.

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