Question

The focal length of a lens of dispersive power $0.45$ which should be placed in contact with a convex lens of focal length $84\text{cm}$ and dispersive power $0.21$ to make the achromatic combination from the two lenses (in cm) is

• A. $+180\text{cm}$
• B. $-180\text{cm}$
• C. $+150\text{cm}$
• D. $-150\text{cm}$

Answer 1

The correct option is B $-180\text{cm}$

We know that the condition of achromatism is
$\frac{{\omega }_1}{f_1}+\frac{{\omega }_2}{f_2}=0$
$\Rightarrow \frac{0.45}{f_1}+\frac{0.21}{84}=0$
$\Rightarrow f_1=-180\text{cm}$