$A$ 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).

For a prism of apex angle $45^o$,it is found that the angle of emergence is $45^o$ for grazing incidence. Calculate the refractive index of the prism.

$A$ ray of light is incident on a right-angled isosceles prism parallel to its base as shown in the figure. The refractive index of the material of the prism is $\sqrt{2}$. Which of the following statement$(s)$ is/are true?

In the diagram,the ray passing through the prism is parallel to the base. The refractive index of the material of the prism is:

For a prism with a prism angle of $60^\circ$ and a refractive index of $\mu = \sqrt{2}$,the angle of minimum deviation is .......... $^\circ$.

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 $\Delta n=2.8 \times 10^{-3}$