# Dispersion of light in a prism confusing!

## Main Question or Discussion Point

I understand that as the frequency of an electromagnetic wave increases, its refractive index decreases in a material. According to this, red light would have a higher refractive index than blue light (is my mistake here? why?).

Since sinI/sinR = n (where I is the angle of incidence, R is the angle of refraction, n is the refractive index), and if I is a constant, for red light R would be smaller than that in blue light.

If so, then when a beam of white light shines into an upright triangular prism, inside the prism the red light should be 'below' the blue light.

But this is contrary to the picture depicted here: http://en.wikipedia.org/wiki/File:Dispersion_prism.jpg" [Broken]

Where is my fault?

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## Answers and Replies

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I understand that as the frequency of an electromagnetic wave increases, its refractive index decreases in a material. According to this, red light would have a higher refractive index than blue light (is my mistake here? why?).

Since sinI/sinR = n (where I is the angle of incidence, R is the angle of refraction, n is the refractive index), and if I is a constant, for red light R would be smaller than that in blue light.

If so, then when a beam of white light shines into an upright triangular prism, inside the prism the red light should be 'below' the blue light.

But this is contrary to the picture depicted here: http://en.wikipedia.org/wiki/File:Dispersion_prism.jpg" [Broken]

Where is my fault?
Blue light has the greater refractive index and I suspect you are getting frequency mixed up with wavelength in your first sentence.Try googling the Cauchy dispersion formula for greater clarification

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So then there is a mistake in this MIT ocw material http://ocw.mit.edu/NR/rdonlyres/Physics/8-02Electricity-and-MagnetismSpring2002/BB80210A-AC60-443D-9DF2-3E3658AE6812/0/speedlight.pdf" [Broken]?

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I clicked but couldn't get into it because of compatibility issues.To a fairly good first approximation the refractive index of glass varies with wavelength in accordance with the following equation:

n=A+B/W^2 ........ A and B are constants and W=wavelength.As you can see as W increases(f decreases) n decreases

Redbelly98
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Homework Helper
So then there is a mistake in this MIT ocw material http://ocw.mit.edu/NR/rdonlyres/Physics/8-02Electricity-and-MagnetismSpring2002/BB80210A-AC60-443D-9DF2-3E3658AE6812/0/speedlight.pdf" [Broken]?
That link is probably correct. However, if you look at the refractive index for visible wavelengths (0.4 - 0.7 μm), it does decrease as the wavelength gets longer:

http://refractiveindex.info/figures/figures_RI/LIQUIDS_Water_20.0C.png [Broken]
Refractive index of water