The length of a vertical pole at the surface of a lake of water $\left(\mu = \frac{4}{3}\right)$ is $24 \, cm$. Then,to an underwater fish just below the water surface,the tip of the pole appears to be ......... $cm$ above the surface.

$A$ large square container with thin transparent vertical walls and filled with water (refractive index $\mu = \frac{4}{3}$) is kept on a horizontal table. $A$ student holds a thin straight wire vertically inside the water at a distance of $12 \ cm$ from one of its corners,as shown in the figure. Looking at the wire from this corner,another student sees two images of the wire,located symmetrically on each side of the line of sight. The separation (in $cm$) between these images is:

$A$ ray of light is incident on the surface of separation of a medium at an angle of $45^\circ$ and is refracted in the medium at an angle of $30^\circ$. What will be the velocity of light in the medium?

$A$ circular disc of radius $R$ is placed co-axially and horizontally inside an opaque hemispherical bowl of radius $a$ (See figure). The far edge of the disc is just visible when viewed from the edge of the bowl. The bowl is filled with a transparent liquid of refractive index $\mu$ and the near edge of the disc becomes just visible. How far below the top of the bowl is the disc placed?

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 $E$?

The phase difference between the incident wave and the reflected wave is $180^o$ when a light ray: