$A$ luminous object is placed $20 \, cm$ from the surface of a convex mirror and a plane mirror is adjusted in such a way that the virtual images formed by the two mirrors coincide. If the focal length of the convex mirror is $5 \, cm$,then the distance between the plane mirror and the object will be......$cm$.

Which of the following phenomena are involved in the formation of a rainbow?

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?

$A$ point source is placed at a distance of $15 \, cm$ from a converging (convex) lens of focal length $10 \, cm$. At what distance (in $cm$) should a convex mirror of focal length $12 \, cm$ be placed so that the image is formed on the object itself?

Write the names of instruments developed by the use of properties of reflection and refraction of mirrors,lenses,and prisms.

The inverse square law for illuminance is valid for: