Pt. 1 White light passes from polystyrene to air, with an incident angle of 29.1

Question

Pt. 1 White light passes from polystyrene to air, with an incident angle of 29.1°. Find the angle between the colours blue (470 nm) and red (660 nm).

Pt. 2 At what distance from the polystyrene surface are the two colours 1.00 mm apart?

ndex of refraction for various media and wavelengths (nm)

Red Orange Yellow Green Blue Violet 660 610 580 550 470 410
Water 1.331 1.332 1.333 1.335 1.338 1.342
Diamond 2.410 2.415 2.417 2.426 2.444 2.458
Crown glass 1.512 1.514 1.518 1.519 1.524 1.530
Flint glass 1.662 1.665 1.667 1.674 1.684 1.698
Polystyrene 1.488 1.490 1.492 1.493 1.499 1.506
Quartz 1.455 1.456 1.458 1.459 1.462 1.468

Explanation / Answer

a)

by snells law

sin i / sin r = n air / n poly (n air = 1)

i = 29.1 degree will be same for both lights

For blue

sin r = sin 29.1 x nblue

   = 0.486 * 1.499 = 0.729

r = arcsin0.729 = 46.804 degree

similarly for red

sin r = 0.486 *nred =0.486 x 1.488

r = arcsin 0.7236670461 =46.358 degree

angle difference or angle between blue and red = 46.804 -46.358=0.446 degree

= 0.00778 rad

b)

Let x be the distance

x = 1.0 mm

x = 1/0.00778 = 128.535 mm

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