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

$A$ 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 .....

The refractive index of a medium is $\mu$ and the wavelength of light in that medium is $\lambda$. Which of the following proportionality relations is correct?

$A$ 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?

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 $TRUE$?

The velocity of light in diamond is $\left(\frac{5}{12}\right)$ times that in air. The velocity of light in water is $\left(\frac{3}{4}\right)$ times that in air. Find the angle of incidence for a ray of light travelling from water to diamond,given that the angle of refraction $r = 30^{\circ}$ and $\sin 30^{\circ} = \frac{1}{2}$.