Consider a tank made of glass (refractive index $1.5$) with a thick bottom. It is filled with a liquid of refractive index $\mu .$ A student finds that, irrespective of what the incident angle $i$ (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of $\mu$ is:

A convex lens is put $10 \mathrm{cm}$ from a light source and it makes a sharp image on a screen, kept $10 \mathrm{cm}$ from the lens. Now a glass block (refractive index $1.5$) of $1.5 \mathrm{cm}$ thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance $d$. Then $d$ is:

An object is at a distance of $20 \mathrm{m}$ from a convex lens of focal length $0.3 \mathrm{m}$. The lens forms an image of the object. If the object moves away from the lens at a speed of $5 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$, the speed and direction of the image will be:

What is the position and nature of the image formed by the lens combination shown in the figure? $\left(f_1, f_2\right.$ are focal lengths)

A point source of light $S$ is placed at a distance $L$ in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance $2 L$ as shown below. The distance over which the man can see the image of the light source in the mirror is