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} $



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