Question

The convex glass lens (${\mu }_g=1.5$) has a focal length of $8cm$ when placed in air. What is the focal length of the lens when it is immersed in water? (${\mu }_k=\frac{4}{3}$)

• A. $32cm$
• B. $6cm$
• C. $16cm$
• D. $30cm$

Answer 1

The correct option is A $32cm$

$\begin{array}{c}\text{By using formula of focal length}\to \\ \Rightarrow \frac{1}{f}=(\frac{{\mu }_1}{{\mu }_2}-1)(\frac{1}{R_1}-\frac{1}{R_2})\end{array}$

$\Rightarrow \frac{1}{8}=\left(\frac{4\cdot 5-4}{1}\right)(\frac{1}{R_1}-\frac{1}{R_2})$

(1) $]\to$ in air

$\Rightarrow \frac{1}{f}=(\frac{1.5}{1.33}-1)(\frac{1}{R_1}-\frac{1}{R_2})-\left(2\right)$

is water

$\Rightarrow \frac{\frac{1}{8}}{\frac{1}{f}}=\frac{\left(\frac{1}{2}\right)}{\frac{\left(1.17\right)}{\left(1.33\right)}}\Rightarrow$

$f=\frac{4\left(1.33\right)}{\left(0.17\right)}$

$f=32cm$

Hence obtion $A$ is correct