JEE PYQ: Ray Optics Question 4
Question 4 - 2021 (17 Mar Shift 1)
The thickness at the centre of a plano convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is $2 \times 10^8$ ms$^{-1}$. The focal length of the lens is
(1) 0.30 cm
(2) 15 cm
(3) 1.5 cm
(4) 30 cm
Show Answer
Answer: (4)
Solution
$R^2 = r^2 + (R - t)^2$ $R^2 = r^2 + R^2 + t^2 - 2Rt$ Neglecting $t^2$, we get $R = \frac{r^2}{2t}$ $\therefore \frac{1}{f} = (\mu - 1)\left(\frac{1}{R} - \frac{1}{\infty}\right) = \frac{\mu - 1}{R}$ $f = \frac{R}{\mu - 1} = \frac{r^2}{2t(\mu - 1)} = \frac{(3 \times 10^{-2})^2}{2 \times 3 \times 10^{-3} \times (\frac{3}{2} - 1)}$ $= \frac{9 \times 10^{-4}}{6 \times 10^{-3} \times 1} \times 2$ $f = 0.3$ m $= 30$ cm
BETA
