Optics Question 823
Question: Two identical thin Plano convex lenses of refractive index n are silvered, one on the plane side and the other on the convex side. The ratio of their focal lengths is
Options:
A) $ \frac{n}{n-1} $
B) $ \frac{n-1}{n} $
C) $ \frac{n+1}{n} $
D) $ n $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \frac{1}{f}=\frac{2}{f _{e}}+\frac{2}{f _{m}} $
$ f _{m}=\frac{R}{2}\text{ }f _{m}=0 $
$ \frac{1}{f _{e}}=\frac{n-1}{R}\text{ }f _{e}=\frac{n-1}{R}\text{ }f _{2}=\frac{R}{2n} $
$ f _{1}=\frac{R}{2( n-1 )}\text{ Ratio}\frac{f _{1}}{f _{2}}=\frac{n}{n-1} $
