Question

A point object is placed at $30cm$ from a convex glass lens $({\mu }_s=3/2)$ 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 is 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 liquid of refractive index $4/3$
• D. The whole system is immersed in liquid of refractive index $9/8$

Answer 1

Answer: (A), (D)

Another concave lens of focal length $60cm$ is placed is contact with the previous lens
The whole system is immersed in liquid of refractive index $9/8$

Here,

Given , Object distance=$30cm$

Final image will be formed at infinity if,

Object dstance=Focal length

now,

for $u=f_{eq}\to f_{eq}=30cm$

$\frac{1}{f_{eq}}=\frac{1}{f_1}-\frac{1}{f_2}$

$f_1=+20cm$

$\frac{1}{f_2}=\frac{1}{20}-\frac{1}{30}=\frac{-1}{60}$

Hence image will be infinity if concave lens of 60 cm focal length is placed in contact.

Now,

let the lens is kept in a surrounding of refractive index $\mu$

then by lens maker formula,

$\frac{1}{f}=(\frac{{\mu }_L}{{\mu }_M}-1)(\frac{1}{R_1}-\frac{1}{R_2})$

$R=20cm$

$\frac{1}{f}=(\frac{3}{2}-1)\left(\frac{2}{R}\right)\to f=R$

$\frac{1}{f_{eq}}=(\frac{\frac{3}{2}}{\frac{9}{8}}-1)\left(\frac{2}{R}\right)$

$f_{eq}=\frac{3R}{2}=\frac{60}{2}=30cm$

hence image distane is at ifinity when the whole system is immersed

in a surrounding of $\mu =\frac{9}{8}$

Option $\text{A,D}$ is correct.