$A$ convex lens is made of $3$ layers of glass of $3$ different materials as shown in the figure. $A$ point object is placed on its axis. The number of images of the object formed is:

The diameter of the Sun is $1.4 \times 10^9 \, m$ and its distance from the Earth is $10^{11} \, m$. What is the diameter of the image (in $cm$) formed by a convex lens of focal length $2 \, m$?

On which does the convergence capacity of a lens depend?

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

If the aperture of a lens is halved,then the image will be:

When an object of height $12 \ cm$ is placed at a distance from a convex lens, an image of height $18 \ cm$ is formed on a screen. Without changing the positions of the object and the screen, if the lens is moved towards the screen, another clear image is formed on the screen. The height of this image is (in $cm$)