Question

A point object is at $30cm$ from a convex glass lens $\left({\mu }_s=\frac{3}{2}\right)$ of focal length $20cm$. The final image of object will be formed at infinity, if

• A. another concave lens of focal length $60cm$ is placed in contact with the previous lens
• B. another convex lens of focal length $60cm$ is placed at a distance of $30cm$ from the first lens
• C. the whole system is immersed in a liquid of refractive index $4/3$
• D. the whole system is immersed in a liquid of refractive index $9/8$

Answer 1

Answer: (A), (D)

Final image is formed at infinity if the combined focal length of the two lenses (in contact) becomes $30cm$.
Thus, from Lens maker's formula, $\frac{1}{30}=\frac{1}{20}+\frac{1}{f}$
i.e. when another concave lens of focal length $60cm$ is kept in contact with the first lens. Similarly, let $\mu$ be the refractive index of a liquid in which focal length of the given lens becomes $30cm$. Then,
$\frac{1}{20}=\left(\frac{3}{2}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)...(i)$
$\frac{1}{30}=\left(\frac{3/2}{\mu }-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)...(ii)$
From Eqs. (i) and (ii), $\mu =\frac{9}{8}$