Let $\mu_{1}$ and $\mu_{2}$ be the refractive indices of two media. $v_{1}$ and $v_{2}$ are the velocities of light in the media respectively. Which one of the following relations is $TRUE$?

$A$ ray of light is incident on a medium of refractive index $\mu$ at an angle of incidence $i$. On refraction in the medium,$\delta$ is the angle of deviation. Then:

$A$ vessel of height $2d$ is half-filled with a liquid of refractive index $\sqrt{2}$ and the other half with a liquid of refractive index $n$ (the given liquids are immiscible). Then the apparent depth of the inner surface of the bottom of the vessel (neglecting the thickness of the bottom of the vessel) will be

Write two definitions and equations of relative refractive index.

Frosted glass is widely used for translucent windows. The region where a transparent adhesive tape is stuck over the frosted glass becomes transparent. The most reasonable explanation for this is:

Two light beams fall on a transparent material block at points $1$ and $2$ with angles $\theta_1$ and $\theta_2$ respectively,as shown in the figure. After refraction,the beams intersect at point $3$,which is exactly on the interface at the other end of the block. Given: the distance between $1$ and $2$ is $d = 4\sqrt{3} \text{ cm}$ and $\theta_1 = \theta_2 = \cos^{-1}\left(\frac{n_2}{2n_1}\right)$,where $n_2$ is the refractive index of the block and $n_1$ is the refractive index of the outside medium $(n_2 > n_1)$. Find the thickness of the block in $\text{cm}$.