A parallel beam of light containing two wavelengths, 1 = 400 nm and 2 = 650 nm,

Question

A parallel beam of light containing two wavelengths, 1 = 400 nm and 2 = 650 nm, enters the silicate flint glass of an equilateral prism as shown in the figure below ( = 45°). At what angle, relative to the normal, does each beam leave the prism?

A parallel beam of light containing two wavelengths, A1 = 400 nm and 2-650 nm enters the silicate flint glass of an equilateral prism as shown in the figure below = 45° normal, does each beam leave the prism? 01 from the normal 2 from the normal At what angle, relative to t 60

Explanation / Answer

For cilicate flint glass index of refraction of light ofwavelength 400nm is 1.642 and for wavelength 650nm is 1.619.

Now for the surface on the left for the wavelength 400nm wehave

sin45 = (1.642)sin r1

r1 = 25.508

Now the angle of incidence at the right surface of the prismis

i1= 90-(180 -(60 + (90-25.508))) = 34.492

Then (1.642)sin34.492 = sin1

1 = 68.41o

Repeating for the second ray

sin45 = (1.619)sin r1

Then r1 = 25.897

Now the angle of incidence at the right surface of the prismis

i1= 90-(180 -(60 + (90-25.897)))   =34.103

Then (1.619)sin34.103 = sin2

2 = 65.20o

  

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