The optical path of a monochromatic light is the same if it goes through $4.0 \, cm$ of glass or $4.5 \, cm$ of water. If the refractive index of glass is $1.53$,the refractive index of water is:

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:

When light enters glass from vacuum,then the wavelength of light:

The velocity of light in a medium is $1.5 \times 10^8 \ m/s$. Its refractive index will be:

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

$A$ pole is vertically submerged in a swimming pool such that it casts a shadow of length $2.15 \, m$ within the water when sunlight is incident at an angle of $30^{\circ}$ with the water surface. If the swimming pool is filled to a height of $1.5 \, m$,then the height of the pole above the water surface in centimeters is $(\mu_W = 4/3) .........$