Question

A narrow beam of light containing yellow (580 nm) and blue (470 nm) wavelengths goes from polystyrene to air, striking the surface at a 22.5° incident angle.

What is the angle (in degrees) between the colors when they emerge?

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

Answer 1

Given information, angle of incidence 0; = 22.5° (for both the lights) Refractive index of polystyrene. For yellow light My = 1.492 For blue light no = 1.499 Refructive index of aio, n=1. light goes Answer ca): First we will alculate the angle of refraction for both the light. Beam of from polystyrene to air. Apply Snell's law for yellow light, Ny sin di = n sin of 04 = angle of refouction for yellow light. : (1.492) sin 30 = (1) sin Of sin Of = 0.746 Of sint (0.746) (04), = 48.2459 for yellow light Apply Shell's law foo blue light, mbsino; = nsinot 04 = angle of ze fauction for blue light, :: (1.499) sin 30 V sin of sin Of 0.7499 04 - sint (0.7499) (04), 48.586 the angle between the coulours , when they emerge 0-(01), (04) = 48.586*- 48.245 = 0.34 0 for blue light

Answer (b): light sepezuted by lo mon. We know that, tan o = AY 4x where o=0.34° 4y= the light Seperated = 1x10?m 4x = the disternee, the light have to travel = .no i. tan (0.34) -3 1x10 Ax. .. Дх 103 tan (0.34) .. Дх 0.168 m Answer: G) Angle between the colours when they emerge, 0 - 0.34 (b) light have to travel to be sepeduted by l.mm 4x = 0.168 m ..