Q142 / 160 · TS EAMCET 2022 (18 Jul Shift 1) · Physics

A lens is made of glass having an index of refraction $1.5$ . One side of the lens is flat and the other side is convex with a radius $R$ . If an object is placed $60 cm$ , towards the convex side of the lens, the image is formed at $120 cm$ on the other side of the lens. The value of $R$ is

Correct answer
A
$20 cm$
B
$\frac{40}{3} cm$
C
$33 cm$
D
$18 cm$

Solution

Using lens maker's formula,
$\frac{1}{f} = (\frac{μ_{2}}{μ_{1}} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) \Rightarrow \frac{1}{f} = \frac{1}{2} (\frac{1}{R}) \Rightarrow f = 2 R$
Now using lens equation,
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{120} - \frac{1}{- 60} = \frac{1}{2 R} \Rightarrow 2 R = 40 cm \Rightarrow R = 20 cm$

Hence, the correct answer is option: 'A'.

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