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JEE Main 2023 · Physics · Ray and Wave Optics · easy

A coin lies at the bottom of a layer of water 8 cm deep (μ=4/3) covered by a flat glass slab 6 cm thick (μ=3/2), which rests on the water. Viewed…

Numerical answer

A coin lies at the bottom of a layer of water 8 cm8\ \mathrm{cm} deep (μ=4/3\mu=4/3) covered by a flat glass slab 6 cm6\ \mathrm{cm} thick (μ=3/2\mu=3/2), which rests on the water. Viewed almost normally from air above, the coin appears to be at a depth (in cm, below the top of the glass) of
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Answer: 10

For near-normal viewing, each layer contributes real thickness divided by its refractive index (relative to the medium above it, the final medium being air). Glass: 6/1.5=4 cm6/1.5=4\ \mathrm{cm}. Water: 8/43=6 cm8\Big/\dfrac43=6\ \mathrm{cm}. The apparent depth below the top surface is 4+6=10 cm4+6=10\ \mathrm{cm}. The coin therefore appears 4 cm4\ \mathrm{cm} nearer than its actual 14 cm14\ \mathrm{cm}.
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