Monochromatic light of frequency $5 \times 10^{14} \ Hz$ travelling in vacuum enters a medium of refractive index $1.5$. Its wavelength in the medium is ....... $\mathring{A}$.

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)

The ratio of the refractive index of red light to blue light in air is

From the figure shown,establish a relation between $\mu_1, \mu_2, \mu_3$.

$A$ girl standing at point $P$ on a beach wishes to reach a point $Q$ in the sea as quickly as possible. She can run at $6 \, kmh^{-1}$ on the beach and swim at $4 \, kmh^{-1}$ in the sea. She should take the path

Give one example of a substance whose mass density is low but optical density is high.