Question

The focal length of a lens of refractive index $\frac{3}{2}$ is $10cm$ in the air. The focal length of that lens in a medium of refractive index $\frac{7}{5}is$:

• A. $-70cm$
• B. $\frac{10}{7}cm$
• C. $70cm$
• D. $Noneofthese$

Answer 1

The correct option is D $Noneofthese$

Given that,

Focal length of lens$f_1=10cm$

Refractive index ${\mu }_1=1.5$

Refractive index ${\mu }_2=1.4$

Now, for the lens in air

$\frac{1}{f}=(n-1)(\frac{1}{R_1}-\frac{1}{R_2})$

$\frac{1}{10}=(1.5-1)(\frac{1}{R_1}-\frac{1}{R_2}).....\left(I\right)$

For the lens in other medium

$\frac{1}{f}=(n-1)(\frac{1}{R_1}-\frac{1}{R_2})$

$\frac{1}{f}=(1.4-1)(\frac{1}{R_1}-\frac{1}{R_2}).....\left(II\right)$

Now, divided equation (I) by (II)

$\frac{\frac{1}{10}}{\frac{1}{f}}=\frac{0.5}{0.4}$

$f=\frac{0.5\times 10}{0.4}$

$f=12.5cm$

Hence, the focal length for other medium is $12.5cm$