In a thin prism of glass (refractive index $\mu = 1.5$),which of the following relations between the angle of minimum deviation $\delta_m$ and the angle of the prism $A$ (where $A = 2r$ for a thin prism) is correct?

$A$ monochromatic light is incident from air on a refracting surface of a prism of angle $A = 75^{\circ}$ and refractive index $n_0 = \sqrt{3}$. The other refracting surface of the prism is coated by a thin film of material of refractive index $n$ as shown in the figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of $\theta \leq 60^{\circ}$. The value of $n^2$ is:

The angle of prism is $5^o$ and its refractive indices for red and violet colours are $1.5$ and $1.6$ respectively. The angular dispersion produced by the prism is.....$^o$

In the visible region, the dispersive powers and the mean angular deviations for crown and flint glass prisms are $\omega, \omega^{\prime}$ and $d, d^{\prime}$ respectively. The condition for obtaining dispersion without deviation, when the two prisms are combined, is:

$A$ thin prism $P_1$ with angle $4^o$ and made from glass of refractive index $1.54$ is combined with another thin prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of prism $P_2$ is......$^o$

The cross-section of a prism is an equilateral triangle $ABC$ as shown in the figure. The minimum deviation is observed when the angle of incidence is equal to the prism angle. The time taken by light to travel from the midpoint $P$ of $BC$ to $A$ is $..... \times 10^{-10} \, s$. (Given: speed of light in vacuum $= 3 \times 10^8 \, m/s$ and $\cos 30^{\circ} = \frac{\sqrt{3}}{2}$)