Dispersion of light in a prism confusing

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Discussion Overview

The discussion centers around the dispersion of light in a prism, specifically addressing the relationship between the frequency, wavelength, and refractive index of light. Participants explore the implications of these relationships for the behavior of different colors of light as they pass through a prism, questioning common misconceptions and clarifying the underlying physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states that as the frequency of an electromagnetic wave increases, its refractive index decreases, leading to confusion about the relative positions of red and blue light in a prism.
  • Another participant suggests that the first participant may be confusing frequency with wavelength, indicating that blue light has a greater refractive index than red light.
  • A participant questions the accuracy of MIT OpenCourseWare material regarding the refractive index and its dependence on wavelength.
  • Another participant provides a formula for the refractive index of glass as a function of wavelength, noting that as wavelength increases, the refractive index decreases.
  • One participant references external resources to illustrate the refractive index behavior for visible wavelengths, indicating that it decreases as the wavelength gets longer.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between frequency, wavelength, and refractive index, with some suggesting a misunderstanding while others defend the accuracy of existing materials. The discussion remains unresolved regarding the implications of these relationships for the dispersion of light.

Contextual Notes

There are limitations in the discussion regarding the clarity of definitions for frequency and wavelength, as well as the specific conditions under which the refractive index is being evaluated. Some mathematical steps and assumptions about the behavior of light in different media are not fully resolved.

Nanyang
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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"

Where is my fault? :confused:
 
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Nanyang said:
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"

Where is my fault? :confused:
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" ?
 
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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
 
Nanyang said:
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" ?

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
Refractive index of waterhttp://upload.wikimedia.org/wikipedia/en/2/20/Dispersion-curve.png
Refractive index of several glass types
 
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