$A$ ray of light passes from vacuum into a medium of refractive index $n$. If the angle of incidence is twice the angle of refraction,then the angle of incidence in terms of refractive index is

$A$ magician during a show makes a glass lens with $n = 1.47$ disappear in a trough of liquid. What is the refractive index of the liquid? Could the liquid be water?

The refractive index of a material for infrared light is:

$A$ vessel of height $2d$ is half-filled with a liquid of refractive index $\sqrt{2}$ and the other half with a liquid of refractive index $n$ (the given liquids are immiscible). Then the apparent depth of the inner surface of the bottom of the vessel (neglecting the thickness of the bottom of the vessel) will be

$A$ large square container with thin transparent vertical walls and filled with water (refractive index $\mu = \frac{4}{3}$) is kept on a horizontal table. $A$ student holds a thin straight wire vertically inside the water at a distance of $12 \ cm$ from one of its corners,as shown in the figure. Looking at the wire from this corner,another student sees two images of the wire,located symmetrically on each side of the line of sight. The separation (in $cm$) between these images is:

The refractive index of glass is $1.6$ and the speed of light in glass will be . . . . . . . Speed of light in vacuum is $3 \times 10^{8} \,m \,s^{-1}$.