$A$ 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 $.5$)

Electromagnetic waves emanating from a point $A$ (in air) are incident on a rectangular block of material $M$ and emerge from the other side as shown below. The angles $i$ and $r$ are angles of incidence and refraction when the wave travels from air to the medium. Such paths for the rays are possible,

$A$ needle is lying at the bottom of a water tank of height $12 \,cm$. The apparent depth of the needle measured by a microscope is $9 \,cm$. If the water is replaced by a liquid of refractive index of $1.5$ of same height, the distance through which the microscope has to be moved to focus the needle again is (in $\,cm$)

The index of refraction of diamond is $2.0$. The velocity of light in diamond in $cm/s$ is approximately:

$A$ cubical vessel has opaque walls. An observer is located such that she can see only the wall $CD$,but not the bottom. To what height (in $cm$) should water be poured so that she can see an object placed at the bottom at a distance of $10 \, cm$ from the corner $C$? The refractive index of water is $\mu = 1.33 \approx 4/3$.

The $X-Y$ plane is taken as the boundary between two transparent media $M_{1}$ and $M_{2}$. $M_{1}$ in $Z \geq 0$ has a refractive index of $\sqrt{2}$ and $M_{2}$ with $Z < 0$ has a refractive index of $\sqrt{3}$. $A$ ray of light travelling in $M_{1}$ along the direction given by the vector $\overrightarrow{A} = 4\sqrt{3}\hat{i} - 3\sqrt{3}\hat{j} - 5\hat{k}$ is incident on the plane of separation. The value of the difference between the angle of incidence in $M_{1}$ and the angle of refraction in $M_{2}$ will be $....$ degrees.