Question

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

• A. another concave lens of focal length $60\text{cm}$ is placed in contact with the previous lens.
  
• B. another concave lens of focal length $30\text{cm}$ is placed in contact with the previous lens.
  
• C. the whole system is immersed in a liquid of refractive index $\frac{4}{3}$.
  
• D. the whole system is immersed in a liquid of refractive index $\frac{9}{8}$.
  
  

Answer 1

Answer: (A), (D)

the whole system is immersed in a liquid of refractive index $\frac{9}{8}$.



The final image is formed at infinity if the combined focal length of the two lenses (in contact) becomes $30\text{cm}.$
or,
$\frac{1}{30}=\frac{1}{20}+\frac{1}{f}$
$\Rightarrow f=–60\text{cm}$

$i.e.$ when another concave lens of focal length $60\text{cm}$ is kept in contact with the first lens.

Similarly, let $\mu$ be the refractive index of a liquid in which the focal length of the given lens becomes $30\text{cm}$.
Then,
$\frac{1}{20}=(\frac{3}{2}-1)(\frac{1}{R_1}-\frac{1}{R_2})$…..$\left(1\right)$

$\frac{1}{30}=(\frac{3/2}{\mu }-1)(\frac{1}{R_1}-\frac{1}{R_2})$…..$\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$, we get

$\frac{1}{3}=(\frac{3/2}{\mu }-1)$
$\frac{4}{3}=\frac{3}{2\mu }$
$\mu =\frac{9}{8}$

Therefore, options $\left(A\right)$ and $\left(D\right)$ are correct.