Question

Two thin convex lenses of focal length 10 cm and 15 cm are separated by a distance of 10 cm. The focal length of combination is :-

• A. 4.2 cm
• B. 6 cm
• C. 10 cm
• D. 15 cm

Answer 1

The correct option is C 10 cm

Two thin convex lenses of focal length 10 cm and 15 cm are separated by a distance of 10 cm.

Therefore, $f_1=10cm$, $f_2=15cm$, and $d=10cm$.

Let, the focal length of this combination is $F$.

Now, for the given system, we know,

$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1{f}_2}$

So, using the given values,

$\frac{1}{F}=\frac{1}{10}+\frac{1}{15}-\frac{10}{10\times 15}$

Or, $\frac{1}{F}=\frac{1}{10}+\frac{1}{15}-\frac{1}{15}$

Or, $\frac{1}{F}=\frac{1}{10}$

$\therefore F=10cm$

So, the correct answer is - (C) $10cm$