Suppose that on some surreal world, raindrops had a square cross section and alw

Question

Suppose that on some surreal world, raindrops had a square cross section and always fell with one face horizontal. The below figure shows such a falling drop , with a white beam of sunlight incident at %u03B8= 70.0o at point P. The part of the light that enters the drop then travels to point A, where some of it refracts out into the air and the rest reflects. That reflected light then travels to point B, where again some of the light refracts out into the air and the rest reflects. What is the difference in the angles of the red light (n=1.331) and the blue light (n=1.343) that emerge at
a) Point A and
b) Point B?

(The angular difference in the light emerging at, say, point A would be the rainbow's angular width)

Explanation / Answer

given

incident angle @ = 70

from the snells law

n1 sin@1 = n2 sin@2b

    where n2 = 1.343

then @2b = sin^-1 ( 1/1.343 * sin 70. ) = 44.4026

n1 sin@1 = n2 sin@2r

where n2 = 1.331

then @2r = sin^-1 ( 1/1.331 * sin 70) = 44.9107916867

for the refraction angle at the surface . thesae rays strike the second surface at complentary angles to those just caliculated . ta king this into consideration , we again use snells law to caliculate the second   refractions

using snells smillarly

then @3b= sin^-1 ( 1.343* sin (90- %u03B82b)

then@3b= sin^-1 ( 1.3370 * sin (90-44.4026) = 72.78

then @3r= sin^-1 ( 1.3290 * sin (90-44.9107 ) = 70.2554980182

which differs by1.99950198185

which gives the rain bow angular width

b) bothe of the refracteds rays emergs from the bottom side with same angle 70

with which they were incident on the top side does not alter this overall fact light comes into the block at the same angle that it emerges with from the opposite parallel side . there is no difference and thus theres is no rain bow in this case.

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