The angles of incidence and emergence of a light ray passing through a prism of angle $A$ are $i$ and $e$ respectively. The total deviation produced by the prism is

The refractive index of a transparent liquid filled in an equilateral hollow prism is $\sqrt{2}$. The angle of minimum deviation for the liquid will be (in $^{\circ}$)

$A$ prism $(\mu = 1.5)$ has a refracting angle of $30^\circ$. The deviation of a monochromatic ray incident normally on one of its surfaces will be $(\sin 48^\circ 36' = 0.75)$.

It was found that the refractive index of the material of a certain prism varied as $\mu = 1.5 + 0.004 / \lambda^{2}$,where $\lambda$ is the wavelength of light used to measure the refractive index. The same material was then used to construct a thin prism of apex angle $10^{\circ}$. Angles of minimum deviation $\delta_{m}$ of the prism were recorded for the sources with wavelengths $\lambda_{1}$ and $\lambda_{2}$,respectively. Then,

$A$ ray of light passing through a prism $(\mu = \sqrt{3})$ suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then,the angle of prism is ..... (in degrees).

One face of a glass prism is silver-polished. $A$ light ray falls at an angle of $45^{\circ}$ on the other face. After refraction, it is subsequently reflected from the silvered face and then retraces its path. The refracting angle of the prism is $30^{\circ}$. The refractive index of the prism is: