The average size of an Indian face is $24\times 16 {\mathrm{cm}}^2$. Find the minimum size of a plane mirror required to see the face completely by one-eyed man $\left(\mathrm{ii}\right)$ Two-eyed man. Given the distance between two eyes are $4 \mathrm{cm}$.

As shown in the figure, an object $O$ is at the position $(-10, 2)$with respect to the origin $P$. The concave mirror $M_1$ has radius of curvature $30 \mathrm{cm}$. A plane mirror $M_2$ is kept at a distance $40 \mathrm{cm}$ infront of the concave mirror. Considering the first reflection on the concave mirror $M_1$ and second on the plane mirror $M_2$. Find the coordinates of the second image with respect to the origin $P$.

A point source $S$ is moving with a speed of $10 \mathrm{m} {\mathrm{s}}^{-1} \mathrm{in} x-y$ plane as shown in the figure. The radius of curvature of the concave mirror is $4 \mathrm{m}$. Determine the velocity vector of the image formed by paraxial rays. 

A man is standing at the edge of a $1 \mathrm{m}$ deep swimming pool completely filled with a liquid of refractive index $\sqrt{3}/\sqrt{2}$. The eyes of the man are $\sqrt{3 }\mathrm{m}$ above the ground. A coin located at the bottom of the pool appears to be at an angle of depression of $30°$ with reference to the eye of man. Then find horizontal distance (represented by $x$ in the figure) of the coin from the eye of the man.

A beam of parallel rays of diameter $b$ propagates in glass at an angle $\mathrm{\theta }$ to its plane. Find the diameter of the beam when it goes to air through this face $(n_{\mathrm{glass}}=n)$

Two concave mirrors each of focal length $f$ are placed in front of each other co-axially at a distance of $4d$ in a medium of refractive index $n_0$. A plane glass slab of refractive index $n$ and thickness $d$ is placed at a distance of $d$ from $M_1$. A point object $O$ is placed at a distance of $d$ from $M_2$ as shown in the figure. Consider first reflection by $M_2$, then refraction on slab and then reflection by $M_1$. Determine the distance of this image after reflection from $M_1$.

The figure shows the square front face (of side $a$) of a transparent cuboidal block. The thickness or the third dimension of the block is negligible in comparison to $a$. The block has uniform refractive index $\mathrm{\mu }$ equal to $2$. A point source $S$ which can emit light in all directions can move inside the block. It is desired that no light of $S$ should pass through $AB$. Sketch the region in which $\mathrm{S}$ should be present to satisfy this condition.

An insect at point $P$ sees its two images in the water-mirror system as shown in the figure. One image is formed due to direct reflection from the water surface and the other image is formed due to refraction, reflection and again refraction by the water mirror system in order. Find the separation between the two images. Mirror has a focal length $60 \mathrm{cm}. (n_{\mathrm{w}}=4/3)$