Question

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

• A. another concave lens of focal length $60 \, cm$ is placed in contact with the previous lens
• B. another convex lens of focal length $60 \, cm$ is placed at a distance of $30 \,cm$ 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 $30 \,cm$.
Thus, from Lens maker's formula, $\frac{1}{30}=\frac{1}{20}+\frac{1}{f}$
i.e. when another concave lens of focal length $60\, cm$ 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 $30 \,cm$. 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), $\mu=\frac{9}{8}$