A concave mirror has radius of curvature of 40 cm. It is at the… | JEE Main 2019 (12 Apr, Shift 1)

Q60JEE Main 2019 · 12 APR · SHIFT 1Difficult

Combination of Lenses

A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to: (Refractive index of water = 1.33)

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Answer: (d)

Mirror: $f = 20\text{ cm}$ , object (particle) 5 cm from it (mirror formula does not depend on the medium).
$\frac{1}{v} = -\frac{1}{20} + \frac{1}{5} = \frac{3}{20} \Rightarrow v = +6.67\text{ cm}$ (virtual, behind the mirror).
Image depth below the water surface: $5 + 6.67 = 11.67\text{ cm}$ .
Seen from above: $d = \frac{11.67}{1.33} \approx 8.8\text{ cm}$
So the answer is (d) 8.8 cm.

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