$A$ light beam is traveling from Region $I$ to Region $IV$ (Refer Figure). The refractive indices in Regions $I, II, III$ and $IV$ are $n_0, \frac{n_0}{2}, \frac{n_0}{6}$ and $\frac{n_0}{8}$,respectively. The angle of incidence $\theta$ for which the beam just misses entering Region $IV$ is:

$A$ ray of light is incident at an angle of $75^{\circ}$ into a medium having refractive index $\mu$. The reflected and the refracted rays are found to suffer equal deviations in opposite directions. The value of $\mu$ is:

Explain rarer and denser medium.

$A$ 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

In the figure given below,a ray of light travelling in a medium of refractive index $\mu$ passes through two different connected rectangular blocks of refractive indices $\mu_1$ and $\mu_2$ $(\mu_2 > \mu_1)$. The angle of incidence $\theta_1$ is increased slightly. Then,the angle $\theta_2$ is

The incorrect statement about the refractive index for a pair of media is: