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…

Question

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?

MARKS Content Team · Accepted Answer

Correct answer: 01.80. 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 ∴ sinθ=OB/SB=9/12=3/4 sinθ=μ_2μ_1=(μ)/2.4 ∴ 3/4=(μ)/2.4 ⇒μ=1.8

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