As shown,a narrow beam of light is incident onto a semi-circular glass cylinder of radius $R.$ Light can exit the cylinder when the beam is at the centre. When the beam is moved parallel to a distance $d$ from the central line,no light can exit the cylinder from its lower surface. Find the refractive index of the glass.

$A$ ray of light passes from a medium $A$ having refractive index $1.6$ to the medium $B$ having refractive index $1.5$. The value of the critical angle of medium $A$ 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:

What should be the maximum acceptance angle at the air-core interface of an optical fibre if $n_1$ and $n_2$ are the refractive indices of the core and the cladding,respectively?

$A$ ray of light is incident normally on one face of a right-angled isosceles prism. It then grazes the hypotenuse. The refractive index of the material of the prism is

$A$ fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and the fish is $12 \, cm$ below the surface,the radius of this circle in $cm$ is