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A point source S is placed at the bottom of a 12 mm high transparent block of diamond(refractive index = 2.4 ). The block is immersed in an optically rarer liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 18 mm on the top of the block. What is the refractive index of the liquid?

Correct answer

01.80

Step-by-step solution

As the light is passing from optically denser medium to rarer medium, let us assume θ is the critical angle. From Pythagoras theorem, SB = SO 2 + OB 2 = 12 2 + 9 2 = 15   mm ∴   sin θ = OB SB = 9 12 = 3 4 sin θ = μ 2 μ 1 = μ 2 . 4 ∴    3 4 = μ 2 . 4    ⇒ μ = 1 . 8

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