Optics Question 627

Question: A concave lens of glass, refractive index 1.5, has both surfaces of same radius of curvature R. On immersion in a medium of refractive index 1.75, it will behave as a

[IIT-JEE 1999]

Options:

A) Convergent lens of focal length 3.5 R

B) Convergent lens of focal length 3.0 R

C) Divergent lens of focal length 3.5 R

D) Divergent lens of focal length 3.0 R

Show Answer

Answer:

Correct Answer: A

Solution:

$ \frac{f _{l}}{f _{a}}=\frac{ _{a}{\mu _{g}}-1}{ _{l}{\mu _{g}}-1}=\frac{1.5-1}{\frac{1.5}{1.75}-1} $ = $ -\frac{1.75\times 0.50}{0.25}=-3.5 $

$ \therefore f _{l}=-3.5\ f _{a}\Rightarrow f _{l}=+3.5R $ (Q fa = R)

Hence on immersing the lens in the liquid, it behaves as a converging lens of focal length 3.5 R.



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