A convex lens is held $60 \mathrm{cm}$ above the bottom of an empty tank. The image of a point $\text{'}P\text{'}$ (on tank) is formed $30 \mathrm{cm}$ above the lens. Image of same point $\text{'}P\text{'}$ (on tank) shifts by $15 \mathrm{cm}$ when tank is filled with liquid up to height of $40 \mathrm{cm}.$ Refractive index of liquid, is

For the system shown in figure, for what value of $d$ image of point object $\text{'}O\text{'}$ is formed on object itself

For the system shown, if the speed of image formed by the plane mirror is minimum then speed, $v$ of the plane mirror is

A cylindrical parallel beam of light of radius $r$ falls on a thin convex lens of focal length $40 \mathrm{cm}$ and then on a concave lens of focal length $10 \mathrm{cm}$ as shown. Area illuminated by beam on the screen is

Consider the situation shown in the figure. The minimum angle by which the plane mirror $M$ should be rotated about the point of incidence $O$ such that the reflected ray is horizontal is

The concave mirror shown in the figure has focal length of $20 \mathrm{cm}.$ The $y$ coordinate of image of object $O$ will be

A plane mirror whose reflecting surface is parallel to the $y-z$ plane is moving with velocity $4\hat{\mathrm{i}} \mathrm{m} {\mathrm{s}}^{–1}.$ If the velocity of the object is $\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+2\hat{\mathrm{k}}\right) \mathrm{m} {\mathrm{s}}^{–1}$, then the velocity of the image is

A linear object, $AC$ of length, $10 \mathrm{cm}$ is placed along the principal axis of a concave mirror of focal length, $10 \mathrm{cm}$ (see figure). $C$ is the centre of curvature of the mirror. The length of the image is