question_answer

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

A) \[\frac{n}{n-1}\]

B) \[\frac{n-1}{n}\]

C) \[\frac{n+1}{n}\]

D) \[n\]

Correct Answer: A

Solution :

[a] \[\frac{1}{f}=\frac{2}{{{f}_{e}}}+\frac{2}{{{f}_{m}}}\] \[{{f}_{m}}=\frac{R}{2}\text{  }{{f}_{m}}=0\] \[\frac{1}{{{f}_{e}}}=\frac{n-1}{R}\text{     }{{f}_{e}}=\frac{n-1}{R}\text{       }{{f}_{2}}=\frac{R}{2n}\] \[{{f}_{1}}=\frac{R}{2\left( n-1 \right)}\text{        Ratio}\frac{{{f}_{1}}}{{{f}_{2}}}=\frac{n}{n-1}\]