$A$ convex mirror and a concave mirror of radius $10\; cm$ each are placed $15\; cm$ apart facing each other. An object is placed midway between them. If the reflection first takes place in the concave mirror and then in the convex mirror,the position of the final image is:

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:

For the refraction of light through a prism,which of the following statements is correct?

$A$ ray of light strikes a plane mirror $M$ at an angle of $45^{\circ}$ as shown in the figure. After reflection,the ray passes through a prism of refractive index $1.5$ whose apex angle is $4^{\circ}$. The total angle through which the ray is deviated is......$^{\circ}$

Answer the following questions:
$(a)$ You have learnt that plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Explain.
$(b)$ $A$ virtual image,we always say,cannot be caught on a screen. Yet when we 'see' a virtual image,we are obviously bringing it on to the 'screen' (i.e.,the retina) of our eye. Is there a contradiction?
$(c)$ $A$ diver under water,looks obliquely at a fisherman standing on the bank of a lake. Would the fisherman look taller or shorter to the diver than what he actually is?
$(d)$ Does the apparent depth of a tank of water change if viewed obliquely? If so,does the apparent depth increase or decrease?
$(e)$ The refractive index of diamond is much greater than that of ordinary glass. Is this fact of some use to a diamond cutter?

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?