Q. 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 $45\ cm$
Explanation
(b) For achromatic combination $\frac{f_{1}}{f_{2}} = - \frac{\omega_{2}}{\omega_{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 $f_{1} = 30cm,\ f_{2} = - 45cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.