$A$ lamp is hanging at a height of $40\, cm$ from the center of a table. If its height is increased by $10\, cm$,the illuminance on the table will decrease by what percentage?

$A$ point source is placed at a distance of $15 \, cm$ from a converging (convex) lens of focal length $10 \, cm$. At what distance (in $cm$) should a convex mirror of focal length $12 \, cm$ be placed so that the image is formed on the object itself?

$A$ particle is oscillating on the $X-$ axis with an amplitude $2\, cm$ about the point $x_0 = 10\, cm$ with a frequency $\omega $. $A$ concave mirror of focal length $5\, cm$ is placed at the origin (see figure). Identify the correct statements.
$(A)$ The image executes periodic motion
$(B)$ The image executes non-periodic motion
$(C)$ The turning points of the image are asymmetric w.r.t the image of the point at $x = 10\, cm$
$(D)$ The distance between the turning points of the oscillation of the image is $\frac{100}{21}\, cm$

An object $O$ is placed in front of a small plane mirror $M_1$ and a large convex mirror $M_2$ of focal length $f$. The distance between $O$ and $M_1$ is $x$,and the distance between $M_1$ and $M_2$ is $y$. The images of $O$ formed by $M_1$ and $M_2$ coincide. The magnitude of $f$ is

For a candle of $40$ power,the exposure time required for a photographic print at a distance of $0.6 \, m$ is $20 \, s$. What will be the exposure time required for the same print at a distance of $1.2 \, m$ using a candle of $20$ power?

Two light sources with equal luminous intensity are placed at a distance of $1.2\, m$ from each other. Where should a screen be placed between them such that the illuminance on one of its faces is four times that on the other face?