$A$ point source $S$ is placed at the bottom of a transparent block of height $h = 10 \ mm$ and refractive index $n_B = 2.72$. It is immersed in a liquid of lower refractive index $n_L$ as shown in the figure. It is found that the light emerging from the block into the liquid forms a circular bright spot of diameter $D = 11.54 \ mm$ on the top surface of the block. The refractive index of the liquid $n_L$ is:

The phenomenon utilised in an optical fibre is

$A$ ray of light incident parallel to the base $PQ$ of an isosceles right-angled triangular prism $PQR$ suffers two successive total internal reflections at the faces $PQ$ and $QR$ before emerging reversed in direction as shown below. If the refractive index of the material of the prism is $\mu$,then

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:

Consider the ray diagram for the refraction given below. The maximum value of angle $\theta$ for which the light suffers total internal reflection at the vertical surface is:

$A$ transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. $A$ light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $\theta$ for which the light ray grazes along the wall of the rod is