When the rectangular tank, as shown in the figure, is filled to the top with an unknown liquid, an observer with eyes level with the top of the tank can just see the corner E. We have to find the index of refraction of the liquid.
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Solution: Click For PDF Version As shown in the figure for an observer with eyes level with the top of the tank will be able to just the corner E of the tank if the index of refraction of the liquid n is such that for the angle of incidence
the angle of refraction is
 .
Applying the Snell’s law
as the light
is refracted from the liquid into air, and using that
From the geometry of the tank we note that
Therefore, the index of refraction of the liquid in the tank will be
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,
,
we get
.