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-D) Yes,plane and convex mirrors can produce real images. If the object is virtual,i.e.,if the light rays converging at a point behind a plane or convex mirror are intercepted by a screen placed in front of the mirror,a real image is formed.
$(b)$ No,there is no contradiction. $A$ virtual image is formed by diverging light rays. The convex lens of the eye converges these rays onto the retina. Here,the virtual image acts as a real object for the eye lens,which then forms a real image on the retina.
$(c)$ The diver is in a denser medium (water) and the fisherman is in a rarer medium (air). Light rays from the fisherman travel from air to water,bending towards the normal. To the diver,the fisherman appears to be at a greater height,making him look taller.
$(d)$ Yes,the apparent depth changes. When viewed obliquely,the apparent depth decreases compared to viewing it normally.
$(e)$ Yes,it is useful. The refractive index of diamond $(2.42)$ is much higher than that of glass $(1.5)$,resulting in a smaller critical angle. $A$ diamond cutter uses this to ensure total internal reflection,which gives the diamond its characteristic sparkle.