Which of the following is $NOT$ involved in the formation of a secondary rainbow?

An object is placed $20 \, cm$ in front of a convex mirror. $A$ plane mirror is also placed such that the virtual images formed by both mirrors coincide. If the plane mirror is placed $15 \, cm$ from the object,find the focal length of the convex mirror in $cm$.

Correct exposure for a photographic print is $10 \, s$ at a distance of $1 \, m$ from a point source of $20 \, cd$. For an equal fogging of the print placed at a distance of $2 \, m$ from a $16 \, cd$ source,the necessary time for exposure is.......$s$.

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?

$A$ 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:

$A$ movie projector forms an image $3.5 \ m$ long of an object $35 \ mm$ long. Supposing there is negligible absorption of light by the aperture,what is the ratio of the illuminance on the slide to the illuminance on the screen?