Two transparent media having refractive indices 1.0 and 1.5 are… | JEE Main 2023 (8 Apr, Shift 2)

Q55JEE Main 2023 · 8 APR · SHIFT 2Medium

Spherical Surfaces & Thin Lenses

Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature $30\text{ cm}$ . The centre of curvature of surface is towards denser medium and a point object is placed on the principal axis in rarer medium at a distance of $15\text{ cm}$ from the pole of the surface. The distance of image from the pole of the surface is ____________ $\text{cm}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 30

$u = -15$ cm, $R = +30$ cm (centre in denser medium), $\mu_1 = 1$ , $\mu_2 = 1.5$ .
$\frac{1.5}{v} + \frac{1}{15} = \frac{0.5}{30} = \frac{1}{60}$
$\frac{1.5}{v} = \frac{1}{60} - \frac{4}{60} = -\frac{1}{20} \Rightarrow v = -30$ cm (virtual, in rarer medium).
So the image distance is 30 cm.

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