For a candle of $40$ power,the exposure time required for a photographic print at a distance of $0.6 \, m$ is $20 \, s$. What will be the exposure time required for the same print at a distance of $1.2 \, m$ using a candle of $20$ power?

$A$ horizontal parallel beam of light passes through a vertical convex lens of focal length $20 \,cm$ and is then reflected by a tilted plane mirror,so that it converges to a point $I$. The distance $P I$ is $10 \,cm$. $M$ is a point at which the axis of the lens intersects the mirror. The distance $P M$ is $10 \,cm$. The angle which the mirror makes with the horizontal is (in $^{\circ}$)

$A$ concave mirror is placed on a horizontal table,with its axis directed vertically upwards. Let $O$ be the pole of the mirror and $C$ its centre of curvature. $A$ point object is placed at $C$. It has a real image,also located at $C$ (a condition called auto-collimation). If the mirror is now filled with water,the image will be:

Two blocks each of mass $m$ lie on a smooth table. They are attached to two other masses as shown in the figure. The pulleys and strings are light. An object $O$ is kept at rest on the table. The sides $AB$ and $CD$ of the two blocks are made reflecting. The acceleration of the two images formed in those two reflecting surfaces with respect to each other is:

Define a ray and a beam of light.

An object is placed at a distance of $30\,cm$ from a convex lens of focal length $20\,cm$. On the other side of the lens,a convex mirror is placed such that the image formed by the combination coincides with the object itself. If the distance between the lens and the mirror is $20\,cm$,find the focal length of the convex mirror in $cm$.