$A$ girl standing at point $P$ on a beach wishes to reach a point $Q$ in the sea as quickly as possible. She can run at $6 \, kmh^{-1}$ on the beach and swim at $4 \, kmh^{-1}$ in the sea. She should take the path

The refractive index of the material of a crystal is $1.68$ and that of castor oil is $1.2$. When a ray of light passes from oil to the crystal,its velocity will change by a factor of:

The refractive index of glass is $1.6$ and the speed of light in glass will be . . . . . . . Speed of light in vacuum is $3 \times 10^{8} \,m \,s^{-1}$.

The wavelength of light in air and some other medium are respectively ${\lambda_a}$ and ${\lambda_m}$. The refractive index of the medium is:

An opaque sphere of radius $a$ is just immersed in a transparent liquid as shown in the figure. $A$ point source is placed on the vertical diameter of the sphere at a distance $a/2$ from the top of the sphere. One ray originating from the point source after refraction from the air-liquid interface forms a tangent to the sphere. The angle of refraction for that particular ray is $30^{\circ}$. The refractive index of the liquid is:

Immiscible transparent liquids $A, B, C, D$ and $E$ are placed in a rectangular glass container,forming layers based on their densities. The refractive indices of the liquids are given in the table below. The container is illuminated from the side,and a small piece of glass with a refractive index of $1.61$ is gently dropped into the liquid layers. In which liquid will the glass piece not be visible as it descends?
| Liquid | Refractive Index |
| :--- | :--- |
| $A$ | $1.51$ |
| $B$ | $1.53$ |
| $C$ | $1.61$ |
| $D$ | $1.52$ |
| $E$ | $1.65$ |