$A$ glass prism of refractive index $1.5$ is immersed in water (refractive index $4/3$) as shown in the figure. $A$ light beam incident normally on face $AB$ undergoes total internal reflection at face $BC$.

$A$ glass slab has a refractive index ' $\mu$ ' with respect to air,and the critical angle for a ray of light going from glass to air is ' $\theta$ '. If a ray of light is incident from air on the glass with an angle of incidence ' $\theta$ ',then the corresponding angle of refraction is:

At the interface between two materials having refractive indices $n_1$ and $n_2$,the critical angle for reflection of an electromagnetic wave is $\theta_{1C}$. The $n_2$ material is replaced by another material having refractive index $n_3$,such that the critical angle at the interface between $n_1$ and $n_3$ materials is $\theta_{2C}$. If $n_3 > n_2 > n_1$,$\frac{n_2}{n_3} = \frac{2}{5}$,and $\sin \theta_{2C} - \sin \theta_{1C} = \frac{1}{2}$,then $\theta_{1C}$ is:

In the figure shown,for an angle of incidence $45^{\circ}$ at the top surface,what is the minimum refractive index $\mu$ needed for total internal reflection at the vertical face?

The figure shows a mixture of blue,green,and red colored rays incident normally on a right-angled prism. The critical angles of the material of the prism for red,green,and blue are $46^{\circ}$,$44^{\circ}$,and $43^{\circ}$ respectively. The arrangement will separate:

The critical angle of light passing from glass to air is minimum for which wavelength?