Adventures in Space! The Cassini spacecraft is imaging the surface of Enceladus,

Question

Adventures in Space! The Cassini spacecraft is imaging the surface of Enceladus, a moon of Saturn. They detect a glare from what could be a lake on the surface! To find its index of refraction and identify the liquid they turn a polarizing filter on its camera until the glare is completely canceled. They find the glare is completely gone when the angle of Cassini from the lake is 30 degree from the tangent to the surface of Enceladus (see figure). What is the index of refraction n of the liquid that makes up this lake? The Cassini spacecraft is, of course, traveling through space (space is a vacuum). (a) n = Squareroot 2 (b) n = Squareroot 3 (c) n = 3/2 (d) n = 2

Explanation / Answer

this question is an application of brewster's law
so, brewster's angle is the angle at which a light ray of particular polarisation is completely transmitted by the medium of refractive index n
so, theta-b = arctan(n) [ theta-b is taken wrt to normal to surface of reflecting surface]
now givem theta-b = 90 - 30 = 60
so, tan(60) = n = sqroot(3)

option b = sqroot(3)

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