A plane mirror of a circular shape with radius, $r=20 \mathrm{cm}$ is fixed to the ceiling. A bulb is to be placed on the axis of the mirror. A circular area of radius, $R=1 \mathrm{m}$ on the floor, is to be illuminated after the reflection of light from the mirror. The height of the room is, $3\mathrm{m}$. What is the maximum distance (in cm) from the center of the mirror and the bulb so that the required area is illuminated?

In figure shown $AB$ is a plane mirror of length $40 \mathrm{cm}$ placed at a height $40 \mathrm{cm}$ from the ground. There is a light source $S$ at a point on the ground. If the minimum height is $p \mathrm{cm}$ and maximum height is $q \mathrm{cm}$ of a man (eye height) required to see the image of the source if he is standing at a point $A$ on the ground as shown in figure, then find the ratio $\frac{q}{p}$

Two concave mirrors each of radius of curvature $40 \mathrm{cm}$ are placed such that their principal axes are parallel to each other & at a distance of $1 \mathrm{cm}$ to each other. Both the mirrors are at a distance of $100 \mathrm{cm}$ to each other. Consider first reflection at $M_1$ and then at $M_2$, the final coordinates of the image thus formed are $\left(x,-y\right)$, then find $\frac{x}{y}$. Take location of object as the origin.

A fly $F$ is sitting on a glass slab, $A$, $45 \mathrm{cm}$ thick of refractive index $\frac{3}{2}$. The slab covers the top of a container $B$ containing water (Refractive index $\frac{4}{3}$) upto a height of $20 \mathrm{cm}$. The bottom of container is closed by a concave mirror $C$ of radius of curvature $40 \mathrm{cm}$. Find the distance (in $\mathrm{cm}$) of final image from $F$ formed by all refractions and reflection assuming paraxial rays.