$A$ convex mirror of focal length $15 \ cm$ and a concave mirror of focal length $10 \ cm$ are placed facing each other at a distance of $40 \ cm$ apart. $A$ point object is placed between the mirrors on their common axis at a distance of $15 \ cm$ from the concave mirror. The position of the image formed by reflection at the convex mirror will be at a distance of ..... $cm$ from it.

If the polarising angle of a piece of glass for green light is $54.74^o$,then the angle of minimum deviation for an equilateral prism made of the same glass is......$^o$ (Given $\tan 54.74^o = 1.414$)

$A$ container is filled with water $(\mu = 1.33)$ up to a height of $33.25\ cm$. $A$ concave mirror is placed $15\ cm$ above the water level and the image of an object placed at the bottom is formed $25\ cm$ below the water level. The focal length of the mirror is (in $cm$)

$A$ $60 \text{ W}$ bulb is hung over the center of a table of size $4 \text{ m} \times 4 \text{ m}$ at a height of $3 \text{ m}$. The ratio of the intensities of illumination at a point on the center of the edge $(A)$ and at the corner of the table $(B)$ is:

$A$ 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 $\frac{100}{21}\, cm$

Find the luminous intensity of the sun if it produces the same illuminance on the earth as produced by a bulb of $10000 \, cd$ at a distance of $0.3 \, m$. The distance between the sun and the earth is $1.5 \times 10^{11} \, m$.