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 t

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?

TestHub · Accepted Answer

As the light is passing from optically denser medium to rarer medium, let us assume $θ$ is the critical angle.

From Pythagoras theorem,

$SB = \sqrt{{SO}^{2} + {OB}^{2}} = \sqrt{12^{2} + 9^{2}} = 15 mm$

$∴ \sin θ = \frac{OB}{SB} = \frac{9}{12} = \frac{3}{4}$

$\sin θ = \frac{μ_{2}}{μ_{1}} = \frac{μ}{2.4}$

$∴ \frac{3}{4} = \frac{μ}{2.4}$

$\Rightarrow μ = 1.8$

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