A certain kind of glass has an index of refraction of 1.656 for blue light of wa

Question

A certain kind of glass has an index of refraction of 1.656 for blue light of wavelength 435 nm and an index of refraction of 1.617 for red light of wavelength 689 nm. If a beam containing these two colors is incident at an angle of 29.6 degrees on a piece of this glass, what is the angle between the two beams inside the glass? So I found the angle of each color using Snell's, then I subtracted those values but that is not correct. Do we need to use the wavelength? how do you find angle between the beams? You did it right. Just make sure to make your two angles as specific as possible before subtracting them. Go 3-4 decimal places at least.

Explanation / Answer

   According to Snell'slaw      

   n   =   sin i / sin r

Here i   =   angle of incidence,   r   =   angle on refraction,   n   =   refractive index.

for bluelight            nb   =   sinib / sin rb

      1.656 =   sin 29.60 / sin rb

      sinrb   =   0.494 /1.656 =   0.2983

Angle of refraction for bluelight      rb   =   sin-10.2983

                                                        =   17.3540    

for redght            nr  =   sinir/ sin rr

      1.617 = sin29.60 / sin rr

      sinrr  =   0.494 /1.617    =   0.3055

   Angle of refraction for red light      rr =   sin-10.3055

=   17.7860

   Difference inangle   r   =   rr   -   rb   =   17.786 -   17.354

   =   0.432 0

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