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A vessel contains a liquid of refractive index (5)/(3). Inside the liquid, S is a point source which is observed from above the liquid. An opaque disc of radius 1cm is floating on the liquid such that its centre is just above the source. Atthiscircumstances liquid of the vessel is leaving gradually through a hole. What is the depth of the liquid, so that the source no more remains visible from above? |
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Answer» Solution :Let x be the required depth obviously, at this position light rays from the source s must be incident at critical ANGLE `(theta_(C))` at the EDGE of the disc [Fig. 2.70]. `"So", "" sintheta_(c) = (1)/(sqrt(1 + x^(2)))` `"ALSO", "" sintheta_(c) = (1)/(mu) = (3)/(5)` `therefore "" (3)/(5) = (1)/(sqrt(1 + x^(2)))` `or, "" 1 + x^(2) = (25)/(9) or, x = (4)/(3) = 1.33cm` 
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