The angle of a prism is $A$ and its refractive index is $\cot \frac{A}{2}$. The angle of minimum deviation is:

$A$ 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).

$A$ 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).

$A$ ray of light passing through an equilateral prism has a velocity of $2.12 \times 10^8 \text{ m/s}$ in the prism material. The minimum angle of deviation is . . . . . . degrees.

$A$ combination of two prisms,one of flint glass and the other of crown glass,produces dispersion without deviation. The angle of the flint glass prism is $15^\circ$. The net angular dispersion for red and violet light will be ..... (Given: for crown glass $\mu = 1.52, \omega = 0.02$; for flint glass $\mu = 1.65, \omega = 0.03$). (in $^\circ$)

An isosceles glass prism with base angles $40^{\circ}$ is clamped over a tray of water in a position such that the base is just dipped in water. $A$ ray of light incident normally on the inclined face suffers total internal reflection at the base. If the refractive index of water is $1.33$,then the condition imposed on the refractive index $\mu$ of the glass is