The figure shows a ray incident at an angle $i = \pi / 3$. The plot shows the variation of $|r - i|$ versus $k = \frac{\mu_1}{\mu_2}$,where $r$ is the angle of refraction. Based on the graph,which of the following statements is correct?

The object distance $u$,the image distance $v$,and the magnification $m$ in a lens follow certain linear relations. These are:

In an experiment for the determination of focal length of a convex mirror,a convex lens of focal length $20 \ cm$ is placed on an optical bench and an object pin is placed at a distance $30 \ cm$ from the lens. When a convex mirror is introduced in between the lens and the real and inverted image of the object,the final image of the object $O$ is formed at $O$ itself. If the distance between the lens and the mirror is $10 \ cm$,then the focal length of the mirror is.......$cm$

Find the luminous intensity of the sun if it produces the same illuminance on the earth as produced by a bulb of $10000 \, cd$ at a distance of $0.3 \, m$. The distance between the sun and the earth is $1.5 \times 10^{11} \, m$.

If the luminous efficiency of a lamp is $2 \text{ lumen/watt}$ and its luminous intensity is $42 \text{ candela}$,then the power of the lamp is.......$W$

$A$ finite size object is placed normal to the principal axis at a distance of $30 \ cm$ from a convex mirror of focal length $30 \ cm$. $A$ plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is (in $cm$)