Two thin lenses of focal lengths $20 \ cm$ and $25 \ cm$ are placed in contact. The effective power of the combination is (in $D$)

Two thin lenses in contact form an achromatic doublet of power $+2 \text{ D}$. The power of the convex lens is $+5 \text{ D}$. What is the ratio of the dispersive powers of the converging and diverging lenses?

An achromatic convergent lens of focal length $20 \, cm$ is made of two lenses (in contact) of materials having dispersive powers in the ratio of $1 : 2$ and having focal lengths $f_1$ and $f_2$. Which of the following is true?

Two thin convex lenses of focal lengths $30 \ cm$ and $10 \ cm$ are placed coaxially,$1 \ cm$ apart. The power of this combination is (in $D$)

Obtain the equivalent focal length of a combination of thin lenses placed in contact.

The focal length of a lens of dispersive power $0.45$ which should be placed in contact with a convex lens of focal length $84 \,cm$ and dispersive power $0.21$ to make the achromatic combination from the two lenses,in $cm$ is