I How can I derive this relation from Snell's law?

Click For Summary
The discussion centers on deriving a relationship from Snell's law regarding the refraction of white light into its colored components when transitioning from air to another medium. The author notes that for small angles of incidence, the difference in angles of refraction for blue and red light is proportional to the difference in their refractive indices. However, they express difficulty in deriving this proportionality using Snell's law. Participants are encouraged to share their attempts and insights to assist in clarifying this derivation. The conversation highlights the connection between refractive indices and the behavior of light in different media.
Ahmed1029
Messages
109
Reaction score
40
IMG_٢٠٢٢٠٩١٥_٠٣٥٦٣٠.jpg
Here, it's shown how white light, after passing from air to another medium, gets broken down into its constituent coloured rays. Each has its own refractive index in the medium, but it's only shown here red, blue and yellow. The auther comments on this image and says that, for small angles of incidence, the difference between the angles of refraction of blue and red is proportional to the difference of their respective indeces of refraction, which is trivially obtained from snell's law. I however can't derive this proportionality from Snell's law. Can someone help me?
 
Reply
  • Like
Likes Philip Koeck
Science news on Phys.org
What have you tried?
 
Reply
  • Like
Likes vanhees71 and Ahmed1029

Similar threads

I Snell's law from a mechanical model
  • · Replies 12 ·
Replies
12
Views
2K
B Deriving Snell's Law
  • · Replies 1 ·
Replies
1
Views
1K
A How to compute phase gradient from Snell's law?
  • · Replies 1 ·
Replies
1
Views
2K
Birefringence in in uniaxial optical media and Snell's law
  • · Replies 6 ·
Replies
6
Views
4K
Understanding a Generalization of Snell's Law
  • · Replies 19 ·
Replies
19
Views
5K
B Fermat's principle and refraction -- Possible misunderstanding
  • · Replies 42 ·
2
Replies
42
Views
5K
Snell's law for an interface with variable refractive index
  • · Replies 13 ·
Replies
13
Views
4K
Snell's Law: Definition, Equations, Refractive Index & Critical Angle
  • · Replies 1 ·
Replies
1
Views
3K
Fermat's Principle, Snell's Law, and the Prism
  • · Replies 8 ·
Replies
8
Views
3K
I Energy Redistribution in Lorentz Oscillator Model with Pure Radiation Damping
  • · Replies 2 ·
Replies
2
Views
874