Question

Two lenses in contact made of materials with dispersive power in the ratio $2:1$ behaves as an achromatic lens of focal length $10\text{cm}$. The individual focal length of the lenses are:

• A. $5\text{cm},-10\text{cm}$
• B. $-5\text{cm},10\text{cm}$
• C. $10\text{cm},-20\text{cm}$
• D. $-20\text{cm},10\text{cm}$

Answer 1

The correct option is A $5\text{cm},-10\text{cm}$

Condition for achromatism focal length for two lenses are in contact.$\frac{{\omega }_1}{f_1}+\frac{{\omega }_2}{f_2}=0$
$-2=\frac{f_1}{f_2}$
$f_1+2f_2=0$
Effective focal length is
$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$

$\frac{1}{10}=\frac{1}{f_1}+\frac{1}{f_2}$
Put $f_1=-2f_2$ and by solving we get
$f_1=-10\text{cm},f_2=5\text{cm}$
Therefore, the correct answer is (A)