A ray of light is incident at an angle of $60°$ on one face of a prism of prism angle $60°.$ If the emerging ray is perpendicular to the face through which it entered, then refractive index of prism, is

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 rod of length $5 \mathrm{cm}$ is placed longitudinally on the optical axis of concave mirror of focal length, $f=20 \mathrm{cm}$ such that image of one end coincides with itself and the image is diminished. The axial magnification produced by 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

A right-angled glass prism $(\mu =\sqrt{3})$ is kept on a horizontal surface in contact with a vertical plane mirror as shown. A ray of light travelling horizontally retraces its path when transparent liquid of refractive index $\mu$ is filled in the space between prism and mirror. Refractive index, $\mu$ of the liquid 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