Question

A thin bi-convex lens (n=1.5 ) has a focal length of 50 cm in air.When immersed in a transparent liquid , the focal length is measured to be 250 cm.The refractive index of the liquid medium is

• A. 1.33
• B. 1.46
• C. 1.3
• D. 1.36

Answer 1

Answer: (D)

1.36

Using lens maker formula :
$\frac{1}{f}=(\frac{n_2}{n_1}-1)(\frac{1}{R_1}-\frac{1}{R_2})$
where $n_2$ is the refractive index of lens and $n_1$ is that of surrounding medium.
$⟹$ $\frac{f^{\prime }}{f}=\frac{(\frac{n_2}{n_1}-1)}{(\frac{n_2^{\prime }}{n_1^{\prime }}-1)}$
Given : $n_2=n_2^{\prime }=1.5$ $n_1=1$ $f=50cm$ $f^{\prime }=250cm$
$\therefore$ $\frac{250}{50}=\frac{(\frac{1.5}{1}-1)}{(\frac{1.5}{n_1^{\prime }}-1)}$
$⟹n_1^{\prime }=1.36$