Question

A thin concave lens is in contact with a thin convex lens. The ratio of their magnitude of the focal length is $\frac{3}{2}$ and the focal length of the combined lens is $30$ cm. The focal lengths of the individual lenses are

• (A) - 15 cm and + 10 cm
• (B) - 75 cm and + 50 cm
• (C) - 21 cm and + 14 cm
• (D) - 30 cm and + 20 cm

Answer 1

The Correct Option is A

Explanation:
Let $f_1$ and $f_2$ be the focal lengths of the concave lens and the convex lens, respectively.Given:$\left|\frac{f_1}{f_2}\right|=\frac{3}{2}$$\left|\frac{f_2}{f_1}\right|=\frac{2}{3}$$\Rightarrow f_2=-\frac{2}{3}{f}_1\dots$ (i) [focal length of concave lens is-ve]When the lenses are combined, the focal length of the combination is$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}[\text{ where },F$ is the focal length of the combined lens]$\Rightarrow \frac{1}{30cm}=\frac{1}{f_1}-\frac{3}{2f_1}$$\Rightarrow \frac{1}{30cm}=-\frac{1}{2f_1}$$\Rightarrow f_1=-15\mathrm{cm}$Substituting this value of $f_1$ in eq. (i), we get$f_2=-\frac{2}{3}\times -15=10\mathrm{cm}$Thus, $f_1=-15$ cm and $f_2=10$ cmHence, the correct option is (A).