The focal length of the field lens (which is an achromatic combination of two lenses) of telescope is 90 cm. The dispersive powers of the two lenses in the combination are 0.024 and 0.036. The focal lengths of two lenses are

Question

The focal length of the field lens (which is an achromatic combination of two lenses) of telescope is 90 cm. The dispersive powers of the two lenses in the combination are 0.024 and 0.036. The focal lengths of two lenses are (A) 30 cm and 60 cm (B) 30 cm and -45 cm (C) 45 cm and 90 cm (D) 15 cm and 45 cm

Tardigrade Admin · Accepted Answer

For achromatic combination (f1/f2)=-(ω2/ω1)=-(0.036/0.024)=-(3/2) and (1/f1)-(1/f2)=(1/90) Solving above equations we get f1=30 cm, f2=-45 cm

Q. The focal length of the field lens (which is an achromatic combination of two lenses) of telescope is $90 c m$ . The dispersive powers of the two lenses in the combination are $0.024$ and $0.036$ . The focal lengths of two lenses are

30 cm and 60 cm

30 cm and -45 cm

45 cm and 90 cm

15 cm and 45 cm

For achromatic combination
$\frac{f _{1}}{f _{2}} = - \frac{ω _{2}}{ω _{1}} = - \frac{0.036}{0.024} = - \frac{3}{2}$
and $\frac{1}{f _{1}} - \frac{1}{f _{2}} = \frac{1}{90}$
Solving above equations we get
$f_{1} = 30 c m$ , $f_{2} = - 45 c m$

Q. The focal length of the field lens (which is an achromatic combination of two lenses) of telescope is 90cm. The dispersive powers of the two lenses in the combination are 0.024 and 0.036. The focal lengths of two lenses are