Question

The focal length of a convex lens made of flint glass is $15\text{cm}$. To remove its chromatic aberration, it is placed in contact with a concave lens made of crown glass. Find the focal length of the concave lens. The ratio of dispersive powers of flint glass lens to the crown glass lens is $1.5$.

• A. $5\text{cm}$
• B. $30\text{cm}$
• C. $20\text{cm}$
• D. $10\text{cm}$

Answer 1

The correct option is D $10\text{cm}$

Given :
Focal length of a convex lens made of flint glass $\left(f_1\right)=15\text{cm}$

Ratio of dispersive powers of flint glass to crown glass is $\left(\frac{{\omega }_1}{{\omega }_2}\right)=1.5$

To find : The focal length of the concave lens $\left(f_2\right)$

For achromatic combination,
$\frac{f_1}{f_2}=-\frac{{\omega }_1}{{\omega }_2}$

$\Rightarrow \frac{15}{f_2}=-1.5$

$\Rightarrow f_2=-10\text{cm}$

Here, negative sign indicates that the lens used is concave lens.

Hence, option $\left(d\right)$ is the correct answer.