Optics Question 821
Question: A thin convex lens of focal length 10 cm and refractive index 1.5 is cut vertically into two equal pieces. They are placed as shown with a liquid of refractive index 3 between them. What is the focal length of the combination?
Options:
A) -10cm.
B) -10/4 cm.
C) -10/3 cm.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ \frac{1}{f}=( \mu -1 )( \frac{1}{R _{1}}-\frac{1}{R _{2}} ); $
$ R=10cm. $
$ \frac{1}{f’}=( 3-1 )( \frac{1}{-10}-\frac{1}{10} ), $
$ f’=-\frac{10}{4} $
$ \frac{1}{f _{eq}}=\frac{1}{20}-\frac{4}{10}+\frac{1}{20}=\frac{2}{20}-\frac{4}{10}\Rightarrow f _{eq}=-\frac{10}{3} $
