PLEASE ANSWER PARTS B AND C! A very narrow beam of white light is incident at 59

Question

PLEASE ANSWER PARTS B AND C! A very narrow beam of white light is incident at 59.50° onto the top surface of a rectangular block of flint glass 14.0 cm thick. The indices of refraction of the glass for red and violet light are 1.639 and 1.661, respectively.

A. Calculate the dispersion angle (i.e., the difference between the directions of red and violet light within the glass block).
4.680×10-1 deg

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).

Explanation / Answer

A) Using Snell's Law we have n_a *sin(i) = n_b*sin(r)
for voilet light

1*sin(59.50) = 1.661*sin(r)

r = arcsin(sin(59.50)/1.661) = 31.24 degree

and for red r = arcsin(sin(59.50)/1.639) = 31.71 degree

So the dispersion angle is 31.71- 31.24 = 0.475 degree

B.)The violet beam will strike the bottom of the glass at = 14.0cm*tan(31.24) = 8.49cm
and the red beam strikes at 14.0cm*tan(31.71) = 8.64cm

So the beam is 6.379 - 6.265 = 0.1599cm wide

C) Beams will be refracted back at 59.50 degree

So the distance across the beam will be the separation distance times the cos(59.50)
= 0.1599cm*cos(59.50) = 0.08118cm

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