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A small coin is resting on the bottom of...

A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels upto the surface of the liquid and moves along its surface (see figure)

How fast is the light traveling in the liquid ?

Text Solution

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s shown in the figure, a light ray from the coin will not emerge out of liquid if, `igtC`.

In `DeltaSAB,R/h=tanCrArrR=htanCrArrR=h/(sqrt(mu^(2)-1))`
Given , R= 3 cm and h= 4 cm

`therefore 3/4=1/(sqrt(mu^(2)-1))`
`rArrmu^(2)=25/9rArrmu=5/3`
But, `mu=C/v`
`rArr` Speed of light,v=`C/mu=(3xx10^(8))/(5//3)=1.8xx10^(8) ms^(-1)`
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