Question

A certain kind of glass has an index of refraction of 1.660 for blue light of wavelength 440 nm and an index of 1.630 for red light of wavelength 690 nm. If a beam containing these two colors is incident at an angle of 30.0° on a piece of this glass, what is the angle between the two beams inside the glass?

Answer 1

here,

for Blue light

the refractive index , n1 = 1.66

the angle of incidence , i = 30 degree

let the angle of refraction be r1

using snell's law

sin(r1)/sin(i) = 1/n1

sin(r1) /sin(30) = 1/1.66

r1 = 17.52 degree

for red light

the refractive index , n2 = 1.63

the angle of incidence , i = 30 degree

let the angle of refraction be r2

using snell's law

sin(r2)/sin(i) = 1/n2

sin(r2) /sin(30) = 1/1.63

r2 = 17.87 degree

the angle between the two beams inside the glass , r = r2 - r1

r = (17.87 - 17.52 )degree

r = 0.35 degree