$A$ ray of light is incident normally on one face of a $30^{\circ}-60^{\circ}-90^{\circ}$ prism of refractive index $5/3$ immersed in water of refractive index $4/3$ as shown in the figure.

The angle of a prism is $30^o$ and its refractive index is $\sqrt{2}$. One of its surfaces is silvered. At what angle of incidence should a ray be incident on the other surface so that after reflection from the silvered surface,it retraces its path?

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

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.......$^{\circ}$

$A$ thin prism of angle $6^{\circ}$ and refractive index for yellow light $(n_{Y}) = 1.5$ is combined with another prism of angle $5^{\circ}$ and $n_{Y} = 1.55$. The combination produces no dispersion. The net average deviation $(\delta)$ produced by the combination is $(\frac{1}{x})^{\circ}$. The value of $x$ is.......

For a prism of prism angle $\theta=60^{\circ}$,the refractive indices of the left half and the right half are,respectively,$n_1$ and $n_2$ $(n_2 \geq n_1)$ as shown in the figure. The angle of incidence $i$ is chosen such that the incident light rays will have minimum deviation if $n_1=n_2=n=1.5$. For the case of unequal refractive indices,$n_1=n$ and $n_2=n+\Delta n$ (where $\Delta n \ll n$),the angle of emergence $e=i+\Delta e$. Which of the following statement$(s)$ is (are) correct?
$(A)$ The value of $\Delta e$ (in radians) is greater than that of $\Delta n$
$(B)$ $\Delta e$ is proportional to $\Delta n$
$(C)$ $\Delta e$ lies between $2.0$ and $3.0$ milliradians,if $\Delta n=2.8 \times 10^{-3}$
$(D)$ $\Delta e$ lies between $1.0$ and $1.6$ milliradians,if $\Delta n=2.8 \times 10^{-3}$