One face of a prism with a refracting angle of $30^{\circ}$ is coated with silver. $A$ ray incident on the other face at an angle of $45^{\circ}$ is refracted,reflected from the silver-coated face,and retraces its path. The refractive index of the prism is:

$A$ deviation of $2^{\circ}$ is produced in the yellow ray when prisms of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass as $0.02$ and $0.03$ respectively and refractive indices for yellow light for these glasses as $1.5$ and $1.6$ respectively,the refracting angle for the crown glass prism will be $........\,^{\circ}$ (in degrees) (Round off to the nearest integer).

By placing the prism in the minimum deviation position,the images of the spectrum:

For a prism,the angle of the prism is $60^{\circ}$ and the refractive index is $\sqrt{7/3}$. The minimum possible angle of incidence so that the light ray is refracted from the second surface is (in $^{\circ}$)

For an equilateral prism,the angle of incidence and the angle of emergence are each equal to $3/4$ of the prism angle. The angle of deviation is .......... $^o$.

$A$ small angled prism of refractive index $1.6$ gives a deviation of $3.6^{\circ}$. The angle of prism is . . . . . . . (in $^{\circ}$)