An object is placed at a distance of $30\,cm$ from a convex lens of focal length $20\,cm$. On the other side of the lens,a convex mirror is placed such that the image formed by the combination coincides with the object itself. If the distance between the lens and the mirror is $20\,cm$,find the focal length of the convex mirror in $cm$.

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 $1.5 \times 10^{11} \, m$.

Write the names of instruments developed by the use of properties of reflection and refraction of mirrors,lenses,and prisms.

$A$ light ray is incident,at an incident angle $\theta_{1}$,on the system of two plane mirrors $M_{1}$ and $M_{2}$ having an inclination angle $75^{\circ}$ between them (as shown in figure). After reflecting from mirror $M_{1}$,it gets reflected back by the mirror $M_{2}$ with an angle of reflection $30^{\circ}$. The total deviation of the ray will be $\dots$ degree.

When seen in green light,the saffron and green portions of our National Flag will appear to be

Which of the following statements is correct?