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Question:

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index 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 11.54 mm on the top of the block. The refractive index of the liquid is 1.21, 1.3, 1.36, 1.42

1.36

1.42

1.21

1.3

Solution:

For a prism we have, tanθc = r/h ∴ θc = 30°
Also from Snell's law, sinθc = μliquid/μblock ∴ sin30° = μliquid/2.72 ∴ μliquid = 2.72sin30° ∴ μliquid = 1.36