An object is placed $30 \mathrm{cm}$ (from the reflecting surface) in front of a block of glass $10 \mathrm{cm}$ thick having its farther side silvered. The final image is formed at $23.2 \mathrm{cm}$ behind the silvered face. The refractive index of glass is

A ray of light strikes a plane mirror at an angle of incidence $45°$ as shown in the figure. After reflection, the ray passes through a prism of refractive index $1.50$, whose apex angle is $4°$. The angle through which the mirror should be rotated if the total deviation of the ray is to be $90°$ is

A beam of white light is incident on the hollow prism of glass as shown in the figure. Then

Two plane mirrors of length $L$ are separated by distance $L$ and a man $M_2$ is standing at a distance $L$ from the connecting line of mirrors as shown in the figure. A man $M_1$ is walking in a straight line at a distance $2L$ parallel to mirrors at speed $u$, then the man $M_2$ at $O$ will be able to see an image of $M_1$ for the time

In the figure shown a thin parallel beam of light is incident on a plane mirror $m_1$ at a small angle $\mathrm{\theta }$. $m_2$ is a concave mirror of focal length $f$. After three successive reflections of this beam, the $x$ and $y$ coordinates of the image is

The distance between an object and its doubly magnified image by a concave mirror is 

[Assume $f=$ focal length]

In the figure shown, the image of a real object is formed at the point $I$. $AB$ is the principal axis of the mirror. The mirror must be 

In the shown figure $M_1$ and $M_2$ are two concave mirrors of the same focal length $10 \mathrm{cm}$. $AB$ and $CD$ are their principal axes, respectively. A point object $O$ is kept on the line $AB$ at a distance $15 \mathrm{cm}$ from $M_1$. The distance between the mirrors is $20 \mathrm{cm}$. Considering two successive reflections first on $M_1$ and then on $M_2$. The distance of the final image from the line $AB$ is

In the given figure a parallel beam of light is incident on the upper part of a prism of angle $1.8°$ and R.I. $\frac{3}{2}$. The light coming out of the prism falls on a concave mirror of radius of curvature $20 \mathrm{cm}$. The distance of the point (where the rays are focused after reflection from the mirror) from the principal axis is  $\left[\mathrm{use} \mathrm{\pi }=3.14\right]$