JEE PYQ: Ray Optics Question 26
Question 26 - 2020 (07 Jan Shift 2)
A thin lens made of glass (refractive index $= 1.5$) of focal length $f = 16$ cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is $f_l$, then the ratio $f_l/f$ is closest to the integer:
(1) 1
(2) 9
(3) 5
(4) 17
Show Answer
Answer: (2)
Solution
Using lens maker’s formula $\frac{1}{f} = \left(\frac{\mu_g}{\mu_a} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$ Here, $\mu_g$ and $\mu_a$ are the refractive index of glass and air respectively. $\Rightarrow \frac{1}{f} = (1.5 - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$ …(i) When immersed in liquid $\frac{1}{f_l} = \left(\frac{\mu_g}{\mu_l} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$ [Here, $\mu_l$ = refractive index of liquid] $\Rightarrow \frac{1}{f_l} = \left(\frac{1.5}{1.42} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$ …(ii) Dividing (i) by (ii) $\Rightarrow \frac{f_l}{f} = \frac{(1.5 - 1)(1.42)}{0.08} = \frac{1.42}{0.16} = \frac{142}{16} = 9$
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