When an achromatic combination is formed by joining two lenses $A$ and $B$ in contact, then

Question

Professor PC Thomas Classes · Answer

What is Chromatic Aberration?
When white light passes through a single lens, the lens acts like a prism. It bends different colors (wavelengths) by different amounts. Violet light bends the most and focuses closer to the lens, while red light bends the least and focuses further away. This "blur" of colors is called chromatic aberration.
Two lenses of focal length $f_1$ and $f_2$ form an achromatic combination if $\frac{\omega_1}{f_1}+\frac{\omega_2}{f_2}=0 \Longrightarrow \frac{f_1}{f_2}=-\frac{\omega_1}{\omega_2}$
 where $\omega_1$ and $\omega_2$ are their respective dispersive powers.

1. Opposite Nature (+ and - focal lengths)
Since dispersive power ( $\omega$ ) is always a positive value for any material, the only way for the equation to equal zero is if one focal length is positive (convex lens) and the other is negative (concave lens).
- Result: One lens disperses the colors, and the second lens "pulls" them back together.

2. Different Materials (Different $\omega$ )
If you used the same material for both lenses ( $\omega_1=\omega_2$ ), the equation would force $f_1=-f_2$.
- The Problem: If the focal lengths are equal and opposite, the total power of the combination becomes zero ( $P=\frac{1}{f_1}+\frac{1}{-f_1}=0$ ).
- Result: The lenses would cancel each other out completely, acting like a flat piece of glass. To have a lens that actually focuses light while being achromatic, you must use materials with different dispersive powers (typically Crown glass and Flint glass).