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Physics Problem!?? Help!!!?
A) A very narrow beam of white light is incident at 41.30 onto
the top surface of a rectangular block of int glass 14.5 cm
thick. The indices of refraction of the glass for red and violet
light are 1.639 and 1.664, respectively.
Calculate the dispersion angle (i.e., the difference between
the directions of red and violet light within the glass block).
B) How wide is the beam when it reaches the bottom of the
block, as measured along the bottom surface of the block?
C) When the rainbow-colored beam emerges from the bottom
of the block, the exiting rays of light are once again parallel.
Calculate the distance between the exiting red and violet rays
(i.e., the thickness of the rainbow).
A) Using Snell's Law we have n_a *sin(θa) = n_b*sin(θb)
so for red light we have
1*sin(41.30) = 1.639*sin(θb)===> θb = arcsin(sin(41.30)/1.639) = 23.746o
and for violet θb = arcsin(sin(41.30)/1.664) = 23.368o
So the dispersion angle is 23.746 - 23.368 = 0.378o
B) Using trig we see that the violet beam strike the bottom of the glass at 14.5cm*tan(23.368) = 6.265cm
and the red beam strikes at 14.5cm*tan(23.746) = 6.379cm
So the beam is 6.379 - 6.265 = 0.114cm wide
C) when the beams leave the glass they both will be refracted back at 41.30o
So the distance across the beam will be the separation distance times the cos(41.30o)
= 0.114cm*cos(41.30) = 0.0856cm
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