At what angle will a ray of light be incident on one face of an equilateral prism,so that the emergent ray may graze the second surface of the prism $(\mu=2)$ (in $^{\circ}$)?

$A$ prism $ABC$ of angle $30^\circ$ has its face $AC$ silvered. $A$ ray of light incident at an angle of $45^\circ$ at the face $AB$ retraces its path after refraction at face $AB$ and reflection at face $AC$. The refractive index of the material of the prism is

The angle of deviation for a ray passing through the given prism is $30^o$. If one half of the prism is removed,what will be the new angle of deviation in degrees?

$A$ prism having refractive index $\sqrt{2}$ and refracting angle $30^{\circ}$ has one of the refracting surfaces silvered. The beam of light incident on the other refracting surface will retrace its path,if the angle of incidence is $\left[\sin \frac{\pi}{6}=0.5\right]$

$A$ ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to $\frac{3}{4}$ of the angle of the prism. The angle of deviation is (in $^{\circ}$)

$A$ 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).