The dispersive powers of glasses of lenses used in an achromatic pair are in the ratio 5: 3. If the focal length of the concave lens is 15 cm, then the nature and focal length of the other lens would be

Question

The dispersive powers of glasses of lenses used in an achromatic pair are in the ratio 5: 3. If the focal length of the concave lens is 15 cm, then the nature and focal length of the other lens would be (A) convex, 9 cm (B) concave, 9 cm (C) convex, 25 cm (D) concave, 25 cm

Tardigrade Admin · Accepted Answer

Condition for achromatic combination (ω/ω')=-(f/f') (5/3)=(-(-15)/f') ⇒ f'=9 cm Focal length is positive, so it is convex

Q. The dispersive powers of glasses of lenses used in an achromatic pair are in the ratio $5 : 3$ . If the focal length of the concave lens is $15 c m$ , then the nature and focal length of the other lens would be

convex, 9 cm

concave, 9 cm

convex, 25 cm

concave, 25 cm

Condition for achromatic combination
$\frac{ω}{ω ^{'}} = - \frac{f}{f ^{'}}$
$\frac{5}{3} = \frac{- ( - 15 )}{f ^{'}}$
$\Rightarrow f^{'} = 9 c m$
Focal length is positive, so it is convex

Q. The dispersive powers of glasses of lenses used in an achromatic pair are in the ratio 5:3. If the focal length of the concave lens is 15cm, then the nature and focal length of the other lens would be