Question

The two lenses of an achromatic doublet should have

• A. equal powers
• B. equal dispersive powers
• C. equal ratio of their power and dispersive power
• D. sum of the product of their powers and dispersive powers are zero

Hint:

Achromatic doublet condition: \(P_1\omega_1 + P_2\omega_2 = 0\). One lens is converging, the other is diverging.

Answer 1

The Correct Option is D

Step 1: Condition for achromatic combination.
Achromatic doublet means no chromatic aberration.
So dispersion produced by one lens must cancel dispersion of the other lens.
Step 2: Use achromatic condition.
If \(P_1, P_2\) are powers and \(\omega_1, \omega_2\) are dispersive powers, then:
\[ P_1\omega_1 + P_2\omega_2 = 0 \]
Step 3: Match with options.
This clearly means that the sum of (power × dispersive power) of both lenses must be zero.
Final Answer: \[ \boxed{P_1\omega_1 + P_2\omega_2 = 0} \]