An air bubble in a glass slab of refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness of the slab is ______.

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An air bubble in a glass slab of refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness of the slab is 12 cm. Explanation: Given: Refractive index of glass, μ = 1.5 Apparent depth from one side = 5 cm Apparent depth from opposite side = 3 cm Let the actual thickness of the slab be t. When viewed from the top, the apparent depth d1 is related to the real depth by: d1 = t/μ Similarly, from the bottom: d2 = (t - x)/μ But in this case, the air bubble is fixed, and the apparent depths seen from both faces are: x/μ = 5 and (t - x)/μ = 3 Multiplying both equations by μ: x = 7.5 cm and t − x = 4.5 cm Add both: t = x + (t − x) = 7.5 + 4.5 = 12 cm

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