On a glass plate,a light wave is incident at an angle of $60^o$. If the reflected and the refracted waves are mutually perpendicular,the refractive index of the material is:

$A$ light beam is travelling from Region $I$ to Region $IV$ (Refer Figure). The refractive indices in Regions $I$,$II$,$III$,and $IV$ are $n_0$,$\frac{n_0}{2}$,$\frac{n_0}{6}$,and $\frac{n_0}{8}$,respectively. The angle of incidence $\theta$ for which the beam just misses entering Region $IV$ is:

Light travels through a glass plate of thickness $t$ and having refractive index $n$. If $c$ is the velocity of light in vacuum,the time taken by the light to travel this thickness of glass is

$A$ light wave travels through three transparent materials of equal thickness. Rank in order,from the highest to lowest,the indices of refraction $n_1, n_2$ and $n_3$.

$A$ ray of light travels from air to water to glass and again from glass to air. The refractive index of water with respect to air is '$X$', glass with respect to water is '$Y$', and air with respect to glass is '$Z$'. Which one of the following is correct?

$A$ 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