The difference of speed of light in the two media $A$ and $B$ $(v_{A}-v_{B})$ is $2.6 \times 10^{7} \, m/s$. If the refractive index of medium $B$ is $1.47$,then the ratio of refractive index of medium $B$ to medium $A$ is: (Given: speed of light in vacuum $c = 3 \times 10^{8} \, m/s$)

$A$ circular disc of radius $R$ is placed co-axially and horizontally inside an opaque hemispherical bowl of radius $a$ (See figure). The far edge of the disc is just visible when viewed from the edge of the bowl. The bowl is filled with a transparent liquid of refractive index $\mu$ and the near edge of the disc becomes just visible. How far below the top of the bowl is the disc placed?

There are certain materials developed in laboratories which have a negative refractive index. $A$ ray incident from air (medium $1$) into such a medium (medium $2$) shall follow a path given by

$A$ ray of light travelling in air has wavelength $\lambda$,frequency $n$,velocity $v$,and intensity $I$. If this ray enters into water,then these parameters are $\lambda'$,$n'$,$v'$,and $I'$ respectively. Which relation is correct from the following?

$A$ mixture of a pure liquid and a solution in a long vertical column (i.e., horizontal dimensions << vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. $A$ ray of light entering the column at right angles to the vertical is deviated from its original path. Find the deviation in travelling a horizontal distance $d << h$, where $h$ is the height of the column.

If the angle of incidence is twice the angle of refraction in a medium of refractive index $\mu$,then the angle of incidence is