It is desired to make a converging achromatic combination of mean focal length 50 cm by using two lenses of materials $A$ and $B$. If the dispersive power of $A$ and $B$ are in ratio 1:2, the focal lengths of the convex and the concave lenses are respectively

Question

Dr. Abubacker · Accepted Answer

(a) $\frac{\omega_{1}}{\omega_{2}} = \frac{1}{2}$
Now,$\ \frac{f_{1}}{f_{2}} = - \frac{\omega_{1}}{\omega_{2}} = - \frac{1}{2}$
Or $\ f_{2} = - 2f_{1}$
Now, $\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$
$\frac{1}{50} = \frac{1}{f_{1}} + \frac{1}{- 2f_{1}}$
Or $50f = \frac{- 2 + 1}{- 2f_{1}} = \frac{1}{2f_{1}}$
Or $2f_{1} = 50\ $or$\ f_{1} = 25\ cm$
Again $f_{2} = - 2 	imes 25\ $cm$= - 50\ $cm

Q. It is desired to make a converging achromatic combination of mean focal length 50 cm by using two lenses of materials $A$ and $B$. If the dispersive power of $A$ and $B$ are in ratio 1:2, the focal lengths of the convex and the concave lenses are respectively

Explanation

Reviewed by Dr. Abubacker

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