$A$ tank is filled with benzene to a height of $120 \,mm$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $80 \,mm$. The refractive index of benzene is: (in $.5$)

$A$ monochromatic light is travelling in a medium of refractive index $n=1.6$. It enters a stack of glass layers from the bottom side at an angle $\theta=30^{\circ}$. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as $n_m=n-m \Delta n$,where $n_m$ is the refractive index of the $m^{\text{th}}$ slab and $\Delta n=0.1$ (see the figure). The ray is refracted out parallel to the interface between the $(m-1)^{\text{th}}$ and $m^{\text{th}}$ slabs from the right side of the stack. What is the value of $m$?

$A$,$B$ and $C$ are parallel-sided transparent media of refractive indices $n_{1}$,$n_{2}$ and $n_{3}$ respectively. They are arranged as shown in the figure. $A$ ray is incident at an angle $i$ on the surface of separation of $A$ and $B$. After refraction into medium $B$,the ray grazes the surface of separation of media $B$ and $C$. Then,$\sin i$ equals to

$A$ light ray is incident on a glass slab at an angle of incidence of $60^o$. If the angle between the reflected ray and the refracted ray is $90^o$,what is the refractive index of the glass slab?

Which of the following ray diagrams shows physically possible refraction?

$A$ ray of light is incident at an angle of $75^{\circ}$ into a medium having refractive index $\mu$. The reflected and the refracted rays are found to suffer equal deviations in opposite directions. The value of $\mu$ is: