$A$ convex lens of focal length $f$ is cut along the dashed line as shown in the figure. What is the focal length of each part?

Assertion: Two convex lenses joined together cannot produce an achromatic combination.
Reason: The condition for achromatism is $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$,where symbols have their usual meaning.

An achromatic combination of lenses produces

$A$ lens maker has to design an achromatic combination of effective power $-0.5 \, D$. The two types of glasses to be used (say $A$ and $B$) have dispersive powers in the ratio $\omega_A : \omega_B = 3 : 5$. Then the lens made from glass $A$ will have a focal length of ....... $cm$.

What is the focal length of a convex lens of focal length $30 \, cm$ in contact with a concave lens of focal length $20 \, cm$? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

The diagram below shows an object placed at a distance $2f$ in front of a convex lens of focal length $f$. Which of the following represents the positions of the image when $(i)$ a parallel-sided glass block,or $(ii)$ a converging lens of long focal length is inserted between the object and the convex lens?