Question

A lens obeys Snell's law that light bend at each surface by an amount determined by index of refraction of the lens and index of the medium in which the lens is located.
$\frac{1}{f}=(n-1)\left(\frac{1}{R_1}\frac{1}{R_2}\right)$ assume that the lens is surrounded by air. Consider instead a thin lens immersed in a liquid of refractive index $n_{liq.}$

1. Find the focal length $f^{{}^{\prime }}$ in liqiud in terms of $f$.

• A. $f^{{}^{\prime }}=\left[\frac{n_{liq}(n-1)}{n-n_{liq}}\right]f$
• B. $f^{{}^{\prime }}=\frac{n_{liq}}{n-n_{liq}}f$
• C. $f^{{}^{\prime }}=\frac{(n_{liq}-1)}{n-n_{liq}}f$
• D. $f^{{}^{\prime }}=\left(\frac{(n-1)}{n_{liq}-n}\right)f$

Answer 1

Answer: (A)

$f^{{}^{\prime }}=\left[\frac{n_{liq}(n-1)}{n-n_{liq}}\right]f$

$\frac{1}{f}=(n-1)(\frac{1}{R_1}-\frac{1}{R_2})........\left(1\right)$
$\frac{1}{f}(\frac{n}{n_{liq}}-1)(\frac{1}{R_1}-\frac{1}{R_2}).....\left(2\right)$
$dividing\left(1\right)by\left(2\right)$
$f^{{}^{\prime }}=\frac{f(n-1)}{(\frac{n}{n_{liq}}-1)}=\frac{f{n}_{liq}(n-1)}{(n-n_{liq})}$