$A$ prism with refractive index $\mu = 1.5$ has a prism angle of $30^\circ$. If a ray is incident normally on one surface,calculate its deviation. (Given: $\sin(48^\circ 36') = 0.75$)

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

$A$ prism of refractive index $n_{1}$ and another prism of refractive index $n_{2}$ are stuck together (as shown in the figure). $n_{1}$ and $n_{2}$ depend on $\lambda$, the wavelength of light, according to the relation:
${n}_{1}=1.2+\frac{10.8 \times 10^{-14}}{\lambda^{2}} \text{ and } {n}_{2}=1.45+\frac{1.8 \times 10^{-14}}{\lambda^{2}}$
The wavelength for which rays incident at any angle on the interface $BC$ pass through without bending at that interface will be $....\,nm.$

$A$ glass prism of refracting angle $60^{\circ}$ is immersed in a liquid in which the angle of minimum deviation is $30^{\circ}$. The critical angle of glass with respect to the liquid medium is (in $^{\circ}$)

For an equilateral prism,it is observed that when a ray strikes grazingly at one face,it emerges grazingly at the other. Its refractive index will be

$A$ prism of crown glass with a prism angle of $9^{\circ}$ and a prism of flint glass are used to make a direct vision spectroscope. If the refractive indices of crown and flint glass are $1.40$ and $1.60$ respectively,then the refracting angle of the flint glass prism will be.....$^{\circ}$