$A$ lamp is hanging $1 \, m$ above the center of a circular table of diameter $1 \, m$. The ratio of illuminances at the center and the edge is:

$A$ ray of light moving along the vector $\vec{v} = -\hat{i} - 2\hat{j}$ undergoes refraction at an interface of two media,which is the $x-z$ plane. The refractive index for $y > 0$ is $\mu_1 = 2$,while for $y < 0$,it is $\mu_2 = \sqrt{5}/2$. Find the unit vector along which the refracted ray moves.

$A$ 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:

$A$ satisfactory photographic print is obtained when the exposure time is $10 \, s$ at a distance of $2 \, m$ from a $60 \, cd$ lamp. The time of exposure required for the same quality print at a distance of $4 \, m$ from a $120 \, cd$ lamp 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?

$A$ 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.....$cm^2$.