$A$ ray of monochromatic light is incident on one refracting face of a prism of angle $75^o$. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is $\sqrt{2}$,the angle of incidence on the first face of the prism is.......$^o$.

$A$ light ray is incident on a prism of prism angle $60^{\circ}$ such that it undergoes minimum deviation. If the refractive index of the prism is $\sqrt{2}$,then the angle of incidence 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 $\Delta n=2.8 \times 10^{-3}$

The angle of deviation $(\delta)$ vs angle of incidence $(i)$ is plotted for a prism. Pick the correct statement:-

$A$ monochromatic ray of light is incident normally on a thin prism of refracting angle $A$. The ray is deviated through an angle $(1.15)^{\circ}$ in passing through the prism. The ray reflected internally from the second face emerges from the first face making an angle of $(6.3)^{\circ}$ with the incident ray. The refractive index of the prism is

The refractive index of a prism is measured using three lines of a mercury vapour lamp. If $\mu_1, \mu_2$ and $\mu_3$ are the measured refractive indices for these green,blue and yellow lines respectively,then