$A$ mark at the bottom of a liquid appears to rise by $0.1 \ m$. The depth of the liquid is $1 \ m$. The refractive index of the liquid is

Blue light travelling in a vacuum has a wavelength of $450 \ nm$. It enters a medium whose refractive index is $1.5$. What is its frequency in the medium? $(Speed of light in vacuum = 3 \times 10^8 \ m \ s^{-1})$

$A$ ray of monochromatic light is incident on the plane surface of separation between two media $X$ and $Y$ with angle of incidence $i$ in medium $X$ and angle of refraction $r$ in medium $Y$. The given graph shows the relation between $\sin i$ and $\sin r$. If $V_X$ and $V_Y$ are the velocities of the ray in media $X$ and $Y$ respectively, then which of the following is true?

If light passes near a massive object,the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refractive index of the medium given by $n = 1 + \frac{2GM}{rc^2}$,where $r$ is the distance of the point of consideration from the centre of the mass of the massive body,$G$ is the universal gravitational constant,$M$ is the mass of the body,and $c$ is the speed of light in vacuum. Considering a spherical object,find the deviation of the ray from the original path as it grazes the object.

Monochromatic light of wavelength $589 \; nm$ is incident from air on a water surface. What are the wavelength,frequency,and speed of
$(a)$ reflected,and
$(b)$ refracted light? Refractive index of water is $1.33$.

$A$ small coin is fixed at the centre of the base of an empty cylindrical steel container having radius $R=1 \,m$ and height $d=4 \,m$. At time $t=0$,the container starts getting filled with water at a flow rate of $Q=0.1 \,m^3/s$ without disturbing the coin. Find the approximate time $t$ in seconds when the coin will first be seen by the observer $O$ from a height of $H=5.75 \,m$ above and $L=1.5 \,m$ radially away from the coin as shown in the figure. (Take refractive index of water,$n=1.33$ or $4/3$)