When sunlight falls normally on Earth,a luminous flux density (illuminance) of $1.57 \times 10^5 \; lm/m^2$ is produced on Earth. The distance of Earth from the Sun is $1.5 \times 10^8 \; km$. The luminous intensity of the Sun in candela is:

In the figure shown,consider the first reflection at the plane mirror and the second at the convex mirror. $AB$ is the object.

Shown in the figure is a convergent lens placed inside a cell filled with a liquid. The lens has a focal length of $+20\,cm$ when in air and its material has a refractive index of $1.50$. If the liquid has a refractive index of $1.60$,the focal length of the system is......$cm$.

$A$ cube of side $2\, m$ is placed in front of a concave mirror of focal length $1\, m$ with its face $P$ at a distance of $3\, m$ and face $Q$ at a distance of $5\, m$ from the mirror. The distance between the images of face $P$ and $Q$ and the heights of the images of $P$ and $Q$ are:

$A$ diverging lens of focal length $10 \, cm$ is placed $10 \, cm$ 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

An object is placed in front of a convex mirror at a distance of $50 \ cm$. $A$ plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is $30 \ cm$,it is found that there is no gap between the images formed by the two mirrors. The radius of the convex mirror is .......$cm$.