Read the information given below.
It is useful to design lenses of derived focal length using surface of suitable radii of curvature. Lens maker formula helps in finding various unknowns and is widely applied.
A convex lens has 30 cm focal length in air. What is its focal length is a liquid whose refractive index is $\frac{4}{3}$ ? (Given refractive index glass is $\frac{3}{2}$)
Answer & explanation
Correct answer: option 2
The correct answer is option (2) : +120 cm
$\frac{1}{f_{air}}=(\mu_g-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
$\frac{1}{f_{liquid}}=\left(\frac{\mu_g}{\mu_l}-1\right) \left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
$\frac{f_{liq}}{f_{air}}=\frac{\frac{1}{2}}{\frac{1}{8}}=4\left(\mu_g =\frac{3}{2}\text{and}\,\, \mu_l=\frac{4}{3}\right)$
$f_{liq}=4 \times 30 = 120 \, cm$