$A$ diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is $\frac{4}{3}$,and the diver's eyes are $15 \, cm$ below the surface of water. Then the radius of the circle is

'Mirage' is a phenomenon due to

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?

$A$ hemispherical vessel is completely filled with a liquid of refractive index $\mu$. $A$ small coin is kept at the lowest point $(O)$ of the vessel as shown in the figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point $E$ (at the level of the vessel) is . . . . . . .

$A$ glass prism whose cross-section is an isosceles triangle stands with its (horizontal) base in water; the angles that its two equal sides make with the base are each $\theta$. An incident ray of light,above and parallel to the water surface,is totally internally reflected at the glass-water interface and subsequently re-emerges into the air. Take the refractive indices of glass and water to be $\frac{3}{2}$ and $\frac{4}{3}$,respectively. The maximum value of $\cos\theta$ is:

If light travels a distance $x$ in $t_1 \, s$ in air and $10x$ distance in $t_2 \, s$ in a medium,the critical angle of the medium will be