The wavelength of light, while it is passing through water, is $540 \ nm$. The refractive index of water is $\frac{4}{3}$. The wavelength of the same light when it is passing through a transparent medium having a refractive index of $\frac{3}{2}$ is . . . . . . $nm$.

If ${ }_{i} \mu_{j}$ represents the refractive index when a ray goes from medium $i$ to medium $j$,then the product ${ }_2 \mu_1 \times { }_3 \mu_2 \times { }_4 \mu_3$ is equal to:

When light is refracted from a surface, which of its following physical parameters does not change?

The $x-z$ plane separates two media $A$ and $B$ with refractive indices $\mu_1$ and $\mu_2$ respectively. $A$ ray of light travels from $A$ to $B$. Its directions in the two media are given by the unit vectors $\vec{r}_A = a\hat{i} + b\hat{j}$ and $\vec{r}_B = \alpha\hat{i} + \beta\hat{j}$ respectively,where $\hat{i}$ and $\hat{j}$ are unit vectors in the $x$ and $y$ directions. Then:

$A$ light ray enters a solid glass sphere of refractive index $\mu=\sqrt{3}$ at an angle of incidence $60^{\circ}$. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is......

The apparent depth of water in a cylindrical water tank of diameter $2R \ cm$ is reducing at the rate of $x \ cm/minute$ when water is being drained out at a constant rate. The amount of water drained in $c.c./minute$ is: ($n_1 =$ refractive index of air,$n_2 =$ refractive index of water)