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JEE Main 2025 · Physics · Ray and Wave Optics · hard

The base of a vessel is a plane mirror. Water (refractive index 4/3) of depth 8 cm lies on the mirror and is covered by a floating oil layer…

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The base of a vessel is a plane mirror. Water (refractive index 4/34/3) of depth 8 cm8\ \mathrm{cm} lies on the mirror and is covered by a floating oil layer (refractive index 1.51.5) of thickness 6 cm6\ \mathrm{cm}. A small bright object is held in air 5 cm5\ \mathrm{cm} above the oil surface. Viewed from directly above (paraxial rays), the image formed by the mirror appears at a depth below the oil surface of
  1. A. 15 cm15\ \mathrm{cm}
  2. B. 33 cm33\ \mathrm{cm}
  3. C. 25 cm25\ \mathrm{cm}
  4. D. 40 cm40\ \mathrm{cm}
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Answer: (C) 25 cm25\ \mathrm{cm}

For near-normal viewing a layer of thickness tt and index μ\mu appears to have thickness t/μt/\mu. The mirror therefore appears at depth 84/3+61.5=6+4=10 cm\dfrac{8}{4/3}+\dfrac{6}{1.5} = 6+4 = 10\ \mathrm{cm} below the oil surface. The mirror forms an image of the object as far behind it as the object is in front, in apparent terms: the object is 5 cm5\ \mathrm{cm} above the surface, i.e. 5+10=15 cm5+10 = 15\ \mathrm{cm} in front of the apparent mirror. The image therefore appears 15 cm15\ \mathrm{cm} behind the apparent mirror, at a depth 10+15=25 cm10+15=25\ \mathrm{cm} below the oil surface. Ignoring the refraction gives the trap 5+2(14)=335+2(14)=33 cm.
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