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

In the given figure, a plano-concave lens is placed on a paper on which a flower is drawn. How far above its actual position does the flower appear to be?

In figure $\left(\mathrm{i}\right)$, a thin lens of focal length $10 \mathrm{cm}$ is shown. The lens is cut into two equal parts and the parts are arranged as shown in figure $\left(\mathrm{ii}\right)$. An object $AB$ of height $1 \mathrm{cm}$ is placed at a distance of $7.5 \mathrm{cm}$ from the arrangement. The height of the final image will be