Q.a) In case of refraction write down the relation between critical angle and refractive index of the denser medium. b) For minimum deviation δm, assuming that angle of incidence = angle of emergence, show that the refractive index of the material of the prism is μ = sin((δm + A)/2) / sin(A/2), where A is refractive angle of the prism. OR

a) The refractive index of the denser medium relates to the critical angle C by μ = 1/sin C. b) At minimum deviation (with angle of incidence = angle of emergence), the prism formula μ = sin((δm+A)/2)/sin(A/2) follows from the prism's geometry.

a) Critical angle relation: At the critical angle $C$, light travelling from the denser to the rarer medium refracts at 90°. Applying Snell's law at the denser–rarer interface:

$\mu \sin C = 1 \times \sin 90^\circ = 1 \implies \mu = \dfrac{1}{\sin C}$

b) Prism formula at minimum deviation:

For a prism of refracting angle $A$, if $i$ is the angle of incidence, $e$ the angle of emergence, $r_1, r_2$ the angles of refraction at the two faces, and $\delta$ the angle of deviation, geometry gives:

$A = r_1+r_2, \qquad \delta = i+e-A$

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