A transparent cube of side 210 mm contains a small air bubble. Its apparent distance, when viewed from one face of the cube is 100 mm , and when viewed through opposite face is 40 mm. What is the actual distance of the bubble from the second face and what is the refractive index of the material of the cube ?

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Let the bubble be at a distance x from face I , then distance from face II  be (210 – x).

As μ = real depth /apparent depth

Therefore, for face I, μ = x / 100 and

for face II, μ = (210 − x ) / 40

x / 100 = (210 − x ) / 40

x = 150 m m

∴ Actual distance of bubble from face II = 210 − x = 210 − 150 = 60 mm .

μ = x / 100

= 150 /100 = 1.5

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