An initially parallel cylindrical beam travels in a medium of refractive index $\mu(I) = \mu_0 + \mu_2I$,where $\mu_0$ and $\mu_2$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. As the beam enters the medium,it will:

$A$ light of wavelength $\lambda_{1}$ and velocity $C_{1}$ travels from the first medium of refractive index $\mu_{1}$ into the second medium of refractive index $\mu_{2}$. The wavelength and velocity of light in the second medium are $\lambda_{2}$ and $C_{2}$ respectively. The refractive index of the second medium with respect to the first medium is given by:

$A$ 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?

The speed of light is maximum in

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.

$A$ tank is filled with water to a height of $12.5 \, cm$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $9.4 \, cm$. The refractive index of water is .....