$A$ lamp is placed $6.0\; m$ from a wall. On putting a lens between the lamp and the wall at a distance of $1.2\; m$ from the lamp,a real image of the lamp is formed on the wall. The magnification of the image is

You are given two lenses,a converging lens with focal length $+10\, cm$ and a diverging lens with focal length $-20\, cm$. Which of the following would produce a virtual image that is larger than the object?

An object and a screen are fixed on the uprights of an optical bench. The distance between them is $100 \, cm$. $A$ convex lens is placed in between the object and the screen and the position of the lens is so adjusted that the image of the object is formed on the screen at two conjugate positions of the lens. The distance between these conjugate positions of the lens is $40 \, cm$. What is the focal length of the lens in $cm$?

$A$ plano-concave lens is made of glass of refractive index $1.5$ and the radius of curvature of its curved face is $100 \,cm$. What is the power of the lens?

Explain how the image is formed by a thin convex lens and derive the lens maker's formula: $\frac{1}{f} = (n_{21} - 1) \left[ \frac{1}{R_1} - \frac{1}{R_2} \right]$.

The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is $40\,cm$. The area of the image is $9$ times that of the square. The focal length of the lens is........$cm$.