Question

An achromatic combination of lenses can be formed by joining:

• A. $1$ convex lens and $1$ plane mirror
• B. $1$ convex lens and $1$ concave lens
• C. Convex lenses
• D. Concave lenses

Answer 1

The correct option is B $1$ convex lens and $1$ concave lens

When a combination of lenses results in no change in focal length of the lens system for different frequencies of light, it is known as achromatic combination of lenses.

For an achromatic combination of lenses, net dispersive power $=0$

i.e $\frac{{\omega }_1}{f_1}+\frac{{\omega }_2}{f_2}=0$

From the conditions of achromatism,
(1) ${\omega }_1$ and ${\omega }_2$ are positive quantities and ${\omega }_1\ne {\omega }_2$.
and
(2) Focal lengths of the two lenses in contact should have opposite signs.

$\therefore$ we can conclude that options (a) , (c) and (d) are wrong.

So in combination (b), focal length can remain unaffected by variation of focal length with wavelength.

Hence, option (b) is the correct answer.

Why this question? NOTE: A combination of two lenses which produces net zero dispersion is called an achromatic doublet