$A$ hemispherical glass body of radius $10\, cm$ and refractive index $1.5$ is silvered on its curved surface. $A$ small air bubble is $6\, cm$ below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen:

$1\%$ of light of a source with luminous intensity $50 \,cd$ is incident on a circular surface of radius $10 \,cm$. The average illuminance of the surface is: (in $,lux$)

An object is placed at a distance of $30\,cm$ from a convex lens of focal length $20\,cm$. On the other side of the lens,a convex mirror is placed such that the image formed by the combination coincides with the object itself. If the distance between the lens and the mirror is $20\,cm$,find the focal length of the convex mirror in $cm$.

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?

An optical component and an object $S$ placed along its optic axis are given in Column $I$. The distance between the object and the component can be varied. The properties of images are given in Column $II$. Match all the properties of images from Column $II$ with the appropriate components given in Column $I$.

Column $I$	Column $II$
$A$. Concave Mirror	$(p)$ Real image
$B$. Convex Mirror	$(q)$ Virtual image
$C$. Convex Lens	$(r)$ Magnified image
$D$. Concave Lens	$(s)$ Image at infinity

The curvature radii of a concavo-convex glass lens are $20\, cm$ and $60\, cm$. The convex surface of the lens is silvered. With the lens horizontal,the concave surface is filled with water. The focal length of the effective mirror is $(\mu_{\text{glass}} = 1.5, \mu_{\text{water}} = 4/3)$.