$A$ rod of glass $(\mu = 1.5)$ with a square cross-section is bent into the shape shown in the figure. $A$ parallel beam of light falls on the plane flat surface $A$ as shown. If $d$ is the width of a side and $R$ is the radius of the inner circular arc,what is the maximum value of $\frac{d}{R}$ such that the light entering the glass slab through surface $A$ emerges from the glass through $B$?

$A$ light ray is incident normally on one face of a right-angled prism and travels parallel to the base inside the prism. If the refractive index of the prism is $\mu$,what should be the angle $\alpha$ that the hypotenuse makes with the base so that the ray undergoes total internal reflection at the hypotenuse?

The speed of light in two media $c_1$ and $c_2$ are $1.5 \times 10^8 \ m/s$ and $2 \times 10^8 \ m/s$ respectively. If the light undergoes total internal reflection,the critical angle between the two media 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:

Glass 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 $\theta$,the corresponding angle of refraction is:

The phenomenon utilised in an optical fibre is