$A$ horizontal parallel beam of light passes through a vertical convex lens of focal length $20 \,cm$ and is then reflected by a tilted plane mirror,so that it converges to a point $I$. The distance $P I$ is $10 \,cm$. $M$ is a point at which the axis of the lens intersects the mirror. The distance $P M$ is $10 \,cm$. The angle which the mirror makes with the horizontal is (in $^{\circ}$)

Two blocks each of mass $m$ lie on a smooth table. They are attached to two other masses as shown in the figure. The pulleys and strings are light. An object $O$ is kept at rest on the table. The sides $AB$ and $CD$ of the two blocks are made reflecting. The acceleration of the two images formed in those two reflecting surfaces with respect to each other is:

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

$A$ film projector magnifies a $100 \; cm^2$ film strip on a screen. If the linear magnification is $4$,the area of the magnified film on the screen is.....$cm^2$.

Column-$I$ contains a list of mirrors and positions of an object. Match this with Column-$II$ describing the nature of the image formed.