Question

A ray of sunlight is passing from diamond into crown glass; theangle of incidence is 31.00°. Theindices of refraction for the blue and red components of the rayare: blue (n_diamond = 2.444,n_{crown glass} = 1.531), and red(n_diamond = 2.410, n_crownglass = 1.520). Determine the angle between the refractedblue and red rays in the crown glass.

Answer 1

Given that

A ray of sunlight is passing from diamond into crown glass;the angle of incidence is(θ_i) =31.00°

The indices of refraction for the blue and red components ofthe ray are

       Blue(n_diamond =2.444, n_{crown glass} = 1.531),

And Red (n_diamond =2.410, n_{crown glass} = 1.520).

Determine the angle between the refracted blue and red(θ_blue -θ_red) =?

Now when a ray of sunlight is passing from diamond into crownglass then the angle of refraction is given for the bluelight is

                           n_diamondsinθ_i =n_crownsinθ_r

Therefore the refracted angle for the blue light is

                           sinθ_r =   n_diamondsinθ_i /n_crown

                                θ_r=sin^-1(n_diamondsinθ_i/n_crown)

                                   = sin^-1((2.444)sin(31.00°)/1.531)

                                   = sin^-1(0.8221)

                                   = 55.3033⁰

Now when a ray ofsunlight is passing from diamond into crown glass then the angle ofrefraction is given for the red lightis

                           n_diamondsinθ_i =n_crownsinθ_r Therefore the refractedangle for the red light is

                           sinθ_r =   n_diamondsinθ_i/n_crown

                                θ_r=sin^-1(n_diamondsinθ_i/n_crown)

                                   = sin^-1((2.410)sin(31.00°)/1.520)

                                   = sin^-1(0.8166)

                                   = 54.7465⁰
The angle between the refracted blue and red(θ_blue -θ_red) =55.3033⁰ - 54.7465⁰

                                                                                                                     ^{= 0.55680}