Question

A lens is made of flint glass (refractive index $=1.5$ ). When the lens is immersed in a liquid of refractive index $1.25$, the focal length :

• A. increases by a factor of 1.25
• B. increases by a factor of 2.5
• C. increases by a factor of 1.2
• D. decreases by a factor of 1.2

Answer 1

Answer: (B)

Lens-maker's formula is given by
$\frac{1}{f}=\left({}_a{\mu }_g-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)...(i)$
where ${}_a{\mu }_g$ is refractive index of glass w.r.t. air, $R_1$ and $R_2$ are radii of curvature of two surfaces of lens and $f$ is focal length of the lens.
If the lens is immersed in a liquid of refractive index ${\mu }_1$ then
$\frac{1}{f_1}=\left({}_1{\mu }_g-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)...(ii)$
Here, ${}_1{\mu }_g$ is refractive index of glass w.r.t. liquid.
Dividing Eq. (i) by Eq. (ii), we have
$\frac{f_1}{f}=\frac{\left({}_a{\mu }_g-1\right)}{\left({}_1{\mu }_g-1\right)}$
$\Rightarrow \frac{f_1}{f}=\left(\frac{1.5-1}{\frac{1.5}{1.25}-1}\right)$
$\Rightarrow \frac{f_1}{f}=\frac{0.5\times 1.25}{0.25}=2.5$
Hence, focal length increases by a factor of $2.5$.