Two point objects are placed on principal axis of a thin converging lens. One is $20 \mathrm{cm}$ from the lens and other is on the other side of lens at a distance of $40 \mathrm{cm}$ from the lens. The images of both the objects coincide. The magnitude of focal length of the lens is

The given figure shows an object placed in front of a lens of focal length $10$ $\mathrm{cm}$, at a distance $20$$\mathrm{cm}$ from the lens. On the other side, a convex mirror of focal length $5$ $\mathrm{cm}$ (with same principal axis as that of the lens) is placed such that all light rays after refracting through the lens strike the mirror simultaneously. The distance between the mirror and the lens, $x$, is 

In the arrangement of a convex lens and a plane mirror as shown, the final image is created at distance ____________  $\mathrm{cm}$ from the lens.

A diverging lens of focal length $-10 \mathrm{cm}$ is moving towards right with a velocity $5 \mathrm{m} {\mathrm{s}}^{-1}$. An object placed on the principal axis is moving towards left with a velocity $3 \mathrm{m} {\mathrm{s}}^{-1}$. The velocity of the image at the instant when the lateral magnification produced is $\frac{1}{2}$, is (All velocities are with respect to ground)

A diverging lens of focal length $10 \mathrm{cm}$ is placed $10 \mathrm{cm}$ in front of a plane mirror as shown in the figure. Light from a very far away source falls on the lens. The final image is at a distance

In the figure given below, there are two convex lenses $L_1$and $L_2$ having focal lengths of $f_1$ and$f_2$, respectively. The distance between $L_1$ and $L_2$ will be

What should be the value of distance $d$ so that final image is formed on the object itself?

If the central portion of a convex lens is wrapped in black paper as shown in the figure, then

The focal length of a convex lens made from a material of refractive index $1.52$ is $10 \mathrm{cm}$ when placed in air. If it is immersed in carbon disulphide of refractive index $1.68$, then its focal length and nature will be