The graph shows how the magnification $m$ produced by a convex thin lens varies with image distance $v$. What was the focal length of the used lens?

$A$ real object approaches a fixed diverging lens with a constant velocity from infinity along the principal axis. The relative velocity between the object and its image will be

$A$ convex lens of focal length $f$ produces an image $\frac{1}{n}$ times the size of the object. The distance of the object from the lens is:

$A$ white light is falling on a bi-convex lens. Which of the following options represents the correct qualitative behaviour of the focussing of this light?

An object is moving with a velocity $V_O = 4 \text{ cm/sec}$ towards a convex lens of focal length $f = 10 \text{ cm}$. The lens is also moving with a velocity $V_L = 2 \text{ cm/sec}$ in the same direction. At the instant when the object is at a distance of $30 \text{ cm}$ from the lens,find the velocity of the image.

When a convex lens is immersed in a liquid of refractive index equal to $80 \%$ of the refractive index of the material of the lens,the focal length of the lens increases by $100 \%$. The refractive index of the liquid is