The length of the optical path of two media in contact of lengths $d_1$ and $d_2$ with refractive indices $\mu_1$ and $\mu_2$ respectively,is

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.

The refractive index of water in a biology laboratory tank varies as $1.33 + 0.002 / \lambda^2$,where $\lambda$ is the wavelength of light. Small pieces of organic matter of different colours are seen at the bottom of the tank using a travelling microscope. Then,the image of the organic matter appears

When light enters from air to water,then its

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. The speed of light in the medium is

$A$ 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