When the object is at distances $u_1$ and $u_2$ from a lens,the images formed are real and virtual respectively,and both have the same size. Then the focal length of the lens is:

$A$ slanted object $AB$ is placed on one side of a convex lens as shown in the diagram. The image is formed on the opposite side. The angle made by the image with the principal axis is

Sunlight of intensity $1.3 \text{ kW m}^{-2}$ is incident normally on a thin convex lens of focal length $20 \text{ cm}$. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light,in $\text{kW m}^{-2}$,at a distance $22 \text{ cm}$ from the lens on the other side is. . . . .

$A$ convex lens has power $P$. It is cut into two halves along its principal axis. Further,one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in the figure). Choose the incorrect option for the reported pieces.

$A$ concave lens of focal length $f$ produces an image $(1/x)$ of the size of the object. The distance of the object from the lens is:

$A$ boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length $10\, cm$. The diameter of the sun is $1.39 \times 10^9\, m$ and its mean distance from the earth is $1.5 \times 10^{11}\, m$. What is the diameter of the sun's image on the paper?