A narrow beam of light containing yellow (580 nm) and green (550 nm) wavelengths

Question

A narrow beam of light containing yellow (580 nm) and green (550 nm) wavelengths goes from polystyrene to air, striking the surface at a 29° incident angle with respect to the normal.

a) What is the angle in degrees between the colors when they emerge from the polystyrene?

b) How far in meters would they have to travel to be separated by 1.00 mm?

Red Orange Yellow Green Blue Violet Medium (660 nm) (610 nm) (580 nm) (550 nm) (470 nm) (410 nm) 1 1.333 1 1.338 I 1.332 1.335 Water 1.342 1.331 Diamond 2.410 2.415 2.417 2.426 2.444 2.458 Glass, 1.512 1.514 1.518 1.519 1.524 1.530 crown Glass, 1.662 1.665 1.667 1.674 1.684 1.698 flint Polystyrene 1,488 1.490 1.492 1,493 1.499 1.506 Quartz 1.455 l.468 1.456 1.458 1.459 1.462

Explanation / Answer

for yellow

n1*sintheta1 = n2*sintheta2

1.492*sin29= 1*sintheta2

theta2 = 46.327 degrees

for green

n1*sintheta1 = n2*sintheta2'

1.493*sin29 = 1*sintheta2'

theta2' = 46.452 derees

(a)

angle between the colors = theta2' - theta2 = 46.327-46.452= 0.125degrees

(b)

distance of seperation = s = 1mm

X = s/0.125= 8mm----and

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