$A$ thin prism $P_1$ with an angle $6^{\circ}$ and made of glass of refractive index $1.54$ is combined with another prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without average deviation. The angle of prism $P_2$ is $........{}^{\circ}$

$A$ prism has a refracting angle $A$. The second refracting surface of the prism is silvered. $A$ light ray falling on the first refracting surface with an angle of incidence $2A$ reaches the second surface and returns back along the same path due to reflection at the silvered surface. The refractive index of the material of the prism is:

If one face of a prism of prism angle $30^{\circ}$ and refractive index $\mu = \sqrt{2}$ is silvered,the incident ray retraces its initial path. The angle of incidence is.......$^{\circ}$

$A$ prism is made up of material of refractive index $\sqrt{3}$. The angle of the prism is $A$. If the angle of minimum deviation is equal to the angle of the prism,then the value of $A$ is: (in $^{\circ}$)

The angle of a prism is $A$. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$ of the prism is

The angle of deviation produced by a thin prism when placed in air is $\delta_1$ and that when immersed in water is $\delta_2$. The refractive indices of glass and water are $\frac{3}{2}$ and $\frac{4}{3}$ respectively. The ratio $\delta_1 : \delta_2$ is