$A$ $2\,m$ long scale with a least count of $0.2\,cm$ is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at $80\,cm$ mark and $1\,m$ mark, respectively. The image of the object pin on the other side of the lens coincides with the image pin that is kept at $180\,cm$ mark. The $\%$ error in the estimation of focal length 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?

$A$ lamp rated at $100 \, cd$ hangs over the middle of a round table with diameter $3 \, m$ at a height of $2 \, m$. It is replaced by a lamp of $25 \, cd$ and the distance to the table is changed so that the illumination at the centre of the table remains as before. The illumination at the edge of the table becomes $X$ times the original. Then $X$ is

$A$ small lamp is hung at a height of $8 \text{ feet}$ above the centre of a round table of diameter $16 \text{ feet}$. The ratio of intensities of illumination at the centre and at points on the circumference of the table will be

To find the focal length of a convex mirror,a student records the following data:

Object Pin	Convex Lens	Convex Mirror	Image Pin
$22.2 \, cm$	$32.2 \, cm$	$45.8 \, cm$	$71.2 \, cm$

The focal length of the convex lens is $f_1$ and that of the mirror is $f_2$. Taking index correction to be negligibly small,$f_1$ and $f_2$ are close to:

$A$ 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?