Question

For a system of two separated lenses of focal lengths f₁ and f₂, separation for the achromatism should be: 

1. \(\dfrac{f_1-f_2}{2}\)
2. f₁ + f₂
3. f1 - f2
4. \(\dfrac{f_1+f_2}{2}\)

Answer 1

Correct Answer - Option 4 : \(\dfrac{f_1+f_2}{2}\)

Concept:

• Achromatism: It is the phenomenon by virtue of which an object seen in white light through a lens would appear white i.e.there is no colour splitting
  • ​Condition: To achieve achromatism, all colours should be focused at a single point.
    • To produce an achromatic lens, a convex lens with positive chromatic aberration should be combined with a suitable concave lens of negative chromatic aberration so that total chromatic aberration is zero.
  • Application: It is a lens that is designed to limit the effects of chromatic and spherical aberration. 
    • Achromatic lenses are corrected to bring two wavelengths (typically red and blue) into focus on the same plane.

Explanation:

• To minimize chromatic aberration the distance between two lenses should be the average of their focal length.

So, here given focal lengths are f_1​ and f_2​

The average of both the focal lengths is

 \( {f_{avg}} = \frac{{{f_1} + {f_2}}}{2}{\rm{ }}\)