$A$ good photographic print is obtained at a distance of $20 \,cm$ with an exposure time of $2 \,s$. What will be the exposure time required to get an equally good result at a distance of $40 \,cm$?

$A$ plano-convex lens is made of a material of refractive index $n$. When a small object is placed $30 \ cm$ away in front of the curved surface of the lens,an image of double the size of the object is produced. Due to reflection from the curved surface of the lens,another faint image is observed at a distance of $10 \ cm$ away from the lens. Which of the following statement$(s)$ is(are) true?
$(A)$ The refractive index of the lens is $2.5$
$(B)$ The radius of curvature of the convex surface is $45 \ cm$
$(C)$ The faint image is erect and real
$(D)$ The focal length of the lens is $20 \ cm$

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

Amount of light entering into the camera depends upon

In an experiment to determine the focal length of a concave mirror,the object distance is $x$ and the image distance is $y$,both measured from the pole of the mirror. Which of the following graphs correctly represents the relationship between $y$ and $x$?

$A$ plane mirror is placed $22.5\; cm$ in front of a concave mirror of focal length $10\; cm$. An object is placed between the two mirrors such that the images formed by both mirrors coincide. Find the magnification of the image produced by the concave mirror.