The refractive index of medium varies, when $0\le x\le 1,$ as $\mu =\left(2-\frac{x^2}{3}\right),$ where $x$ is in $\mathrm{cm}.$ The optical path length for a ray moving in straight line from $x=0$ to $x=1 \mathrm{cm}$ is

A point object is placed in the arrangement shown. The distance of image formed by lens-$2$ from its optical centre is

An equiconvex lens $(\mu =1.5)$ of focal length $f=20 \mathrm{cm}$ is placed on a plane mirror. A liquid of $\mu =\frac{4}{3}$ is filled between the gap as shown. At what distance from the lens an object should be placed so that a virtual image of double the size of object is formed?

A thin lens is made in the shape of a disc of thickness $d$ and radius $R.$ The refractive index $\left(\mu \right)$ of material of disc varies with distance $r$ from the centre. If parallel beam of light get focused at distance $f>>R$ from the lens, then (refractive index at centre of disc is ${\mu }_0$)

Figure shows a container of width $H.$ A telescope is fitted at a height $H$ above the base on its side wall such that it is focussed at the point $A$ as shown. Now aliquid is poured slowly in the container. The refractive index of liquid is $\mu =\sqrt{2}.$ Select the correctalternatives