$A$ 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 .....

Electromagnetic waves emanating from a point $A$ (in air) are incident on a rectangular block of material $M$ and emerge from the other side as shown below. The angles $i$ and $r$ are angles of incidence and refraction when the wave travels from air to the medium. Such paths for the rays are possible,

$A$ light of wavelength $\lambda_{1}$ and velocity $C_{1}$ travels from the first medium of refractive index $\mu_{1}$ into the second medium of refractive index $\mu_{2}$. The wavelength and velocity of light in the second medium are $\lambda_{2}$ and $C_{2}$ respectively. The refractive index of the second medium with respect to the first medium is given by:

$A$ beaker containing liquid is placed on a table,underneath a microscope which can be moved along a vertical scale. The microscope is focused,through the liquid,onto a mark on the table when the reading on the scale is $a$. It is next focused on the upper surface of the liquid and the reading is $b$. More liquid is added and the observations are repeated; the corresponding readings are $c$ and $d$. The refractive index of the liquid is

An insect starts moving up in a liquid from point $O$ with a variable refractive index $\mu = \mu_0(1 + ay)$,where $y$ is the depth of the liquid from the surface. If $u$ is the speed of the insect,what is its apparent speed to the observer $E$?

$A$ beam of monochromatic light is refracted from vacuum into a medium of refractive index $1.5$. The wavelength of refracted light will be