$A$ beam of light is propagating at an angle $\alpha_1$ from medium $1$ into medium $2$ at an angle $\alpha_2$. If the wavelength of light in medium $1$ is $\lambda_1$,then the wavelength of light in medium $2$,$\lambda_2$,is:

$A$ ray of light strikes a glass plate at an angle of $60^o$. If the reflected and refracted rays are perpendicular to each other,the index of refraction of the glass is:

An infinitely long cylinder of radius $R$ is made of an unusual exotic material with refractive index $-1$ (See figure). The cylinder is placed between two planes whose normals are along the $y$-direction. The center of the cylinder $O$ lies along the $y$-axis. $A$ narrow laser beam is directed along the $y$-direction from the lower plate. The laser source is at a horizontal distance $x$ from the diameter in the $y$-direction. Find the range of $x$ such that light emitted from the lower plane does not reach the upper plane.

$A$ ray of light $AO$ in vacuum is incident on a glass slab at an angle of $60^o$ and refracted at an angle of $30^o$ along $OB$ as shown in the figure. The optical path length of the light ray from $A$ to $B$ is

The refractive index of glass is $3/2$ and the refractive index of water is $4/3$. If the speed of light in glass is $2.00 \times 10^8 \ m/s$,the speed of light in water will be:

When a light ray is incident on a medium at an angle $i$ and refracted into a second medium at an angle $r$,the graph of $\sin r$ vs $\sin i$ is as shown below. From this,one can conclude that:
$(A)$ Velocity of light in the second medium is $1.73$ times the velocity of light in the first medium
$(B)$ Velocity of light in the first medium is $1.73$ times the velocity in the second medium
$(C)$ The critical angle for the two media is given by,$\sin i_c = \frac{1}{\sqrt{3}}$
$(D)$ The critical angle for the two media is given by,$\sin i_c = \frac{1}{2}$