A source of light is placed at a distance of $75 \mathrm{cm}$ from a screen. Two sharp images are formed on screen when a lens is placed between source and screen at two positions. If one image is four times larger than the other, then focal length of the lens used, is

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 an object $O$ kept at $P.$ A plane mirror parallel to $yz$ plane is moving with velocity $3\hat{i} \mathrm{m} {\mathrm{s}}^{-1}.$
Select the correct alternative

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

When the space between two glass lenses in combination shown in figure is filled with water, then

. A point object is placed $30 \mathrm{cm}$ in front of an equiconvex lens of radius of curvature $15 \mathrm{cm}$ and made of glass of refractive index $\frac{3}{2}.$ On placing a convex mirror of radius of curvature $15 \mathrm{cm}$ behind the lens on image side as shown in figure, the final image is found to coincide with the object. The possible distance $\mathrm{x}$ between convex lens and convex mirror is

A converging lens is used to form an image on a screen. When the upper half of the lens is covered by an opaque screen