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 .......$cm$.

$A$ small fish,$0.4\,m$ below the surface of a lake,is viewed through a simple converging lens of focal length $3\,m$. The lens is kept at $0.2\,m$ above the water surface such that the fish lies on the optical axis of the lens. The image of the fish seen by the observer will be at $\left( \mu_{water} = \frac{4}{3} \right)$

$A$ glass sphere of refractive index $1.5$ and radius $40\,cm$ has half its hemispherical surface silvered. The point where a parallel beam of light,coming along a diameter,will focus (or appear to) after coming out of the sphere,will be:

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:

Physical processes are sometimes described visually by lines. Only the following can cross.

$A$ horizontal parallel beam of light passes through a vertical convex lens of focal length $20 \,cm$ and is then reflected by a tilted plane mirror,so that it converges to a point $I$. The distance $P I$ is $10 \,cm$. $M$ is a point at which the axis of the lens intersects the mirror. The distance $P M$ is $10 \,cm$. The angle which the mirror makes with the horizontal is (in $^{\circ}$)