Question

A combination is made of two lenses of focal lengths $f$ and $f^{\prime }$ in contact; the dispersive powers of the materials of the lenses are $\omega$ and ${\omega }^{\prime }$. The combination is achromatic when

• A. $\omega ={\omega }_0,{\omega }^{\prime }=2{\omega }_0,f^{\prime }=2f$
• B. $\omega ={\omega }_0,{\omega }^{\prime }=2{\omega }_0,f^{\prime }=f/2$
• C. $\omega ={\omega }_0,{\omega }^{\prime }=2{\omega }_0,f^{\prime }=-f/2$
• D. $\omega ={\omega }_0,{\omega }^{\prime }=2{\omega }_0,f^{\prime }=-2f$

Answer 1

The correct option is D $\omega ={\omega }_0,{\omega }^{\prime }=2{\omega }_0,f^{\prime }=-2f$

For an achromatic combination of lenses,

$\frac{{\omega }_1}{f_1}+\frac{{\omega }_2}{f_2}=0$

$⟹\frac{\omega }{f}+\frac{{\omega }^{\prime }}{f^{\prime }}=0$

Only option D satisfies the above condition.