Q. An achromatic convergent doublet of two lenses in contact has a power of +2D. The convex lens has power +5 D. What is the ratio of the dispersive powers of the convergent and divergent lenses?
A) 2:5
B) 3:5
C) 5:2
D) 5:3
Explanation
(b) The condition for achromatism is
$\omega_{1}P_{1} + \omega_{2}P_{2} = 0$
$\omega_{1}P_{1} = - \omega_{2}P_{2}$
$\Rightarrow \frac{\omega_{1}}{\omega_{2}} = - \frac{P_{2}}{P_{1}}$
Now, $P_{1} + P_{2} = 2D$
Or $\ 5 + P_{2} = 2\ $or$\ {\ P}_{2} = - 3D$
$\therefore\frac{\omega_{1}}{\omega_{2}} = - \frac{- 3}{5} = \frac{3}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.