Question

If the lens is slivered at one side what will be the new focal length (Given refractive index of lens $=n$ and focal length $=f$) ?

• A. $f^{{}^{\prime }}=\frac{f}{2}$
• B. $f^{{}^{\prime }}=\frac{f\left(n\right)}{4}$
• C. $f^{{}^{\prime }}=\frac{f(n-1)}{2n-1}$
• D. $f^{{}^{\prime }}=\frac{f(n+1)}{(2n-1)}$

Answer 1

The correct option is C $f^{{}^{\prime }}=\frac{f(n-1)}{2n-1}$

$P=2P_L+P_M$

$\frac{1}{f}=\frac{2}{f_L}+\frac{1}{f_m}=\frac{2}{f_L}+\frac{1}{R}.........\left(1\right)$
$\frac{1}{f_L}=(n-1)\frac{2}{R}$
$or\frac{2}{R}=\frac{1}{f_L(n-1)}............\left(2\right)$

From $\left(1\right)and\left(2\right)$
$f^{{}^{\prime }}=\frac{f(n-1)}{2n-1}$