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Homework Help: Dispersion / diffraction

  1. Aug 16, 2005 #1
    i'm getting confused. so when white light diffracts, red light will bend the most and blue light will bend the least. but when white light disperses, blue light will bend the most, but white light will bend the least? i'm not understanding why.

    and also i read somewhere that the angle of diffraction depends on the wavelength, and i want to know how that works out?

    and doesnt' dispersion depend on snells' law, which shouldn't change for different frequencies because it's just n and sin?

    thanks, it's not a specific homework question, i just got confused while working some other stuff out.

    (kay i think i got the diffraction one)
    asin(theta) = m*wavelength,
    thus longer wavelength = longer the angle of diffraction.

    so what's up with the dispersion one now? some tutorial website said frequency would change n, but if n = c/v, why would red light or blue light move faster/slower than one another in a medium?
    Last edited: Aug 16, 2005
  2. jcsd
  3. Aug 16, 2005 #2

    Andrew Mason

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    Diffraction and dispersion are fundamentally different phenomena. Diffraction consists of interference between light waves passing through different parts of a diffraction grating or slit(s). The distance between peaks of maximum intensity on a screen some distance from the grating or slit(s) is due to interference (which is proporational to wavelength), not 'bending'. The distance between interference maxima will be greater with longer wavelength light.

    Dispersion results from the fact that light of different frequencies pass through transparent matter at different effective speeds. This means that the index of refraction is frequency dependent. Blue light has a slower effective speed than red light through glass, so it has a higher index of refraction and bends more than red.

  4. Aug 17, 2005 #3
    so is there a similarity between dispersion and refraction, because refraction deals with snells law?

    there was a question on a practice test i took with the question:

    if two monochromatic beans of red and violet light are shone upon a thin film (n = 1.3), which color of light is deflected the farthest from its original path upon entering the film?

    the answer was both rays are deflected by the same amount because the angle of refraction doesnt' depend on the wavelength of the light.

    so you're saying that n is different for each different type of light and the angle should be dependent on the frequencies of light? how so?

  5. Aug 17, 2005 #4
    To keep it simple :

    Diffraction is the phenomenon where a wave "spreads out" because it passes through a narrow opening (think of pushing on the end of a water hooze)

    Dispersion is the phenomenon where a wave spreads out because it passes through a medium of which the index of refraction varies as the wave passes through it (this is how a rain bow arises).

    After both these phenomena, both constructive and destructive interference can take place depending on the relative phase differences of the different waves involved.

    The 'spreading out' of the wave means that each constituent frequence will bend off or reflect by a different angle. In the case of diffraction, the higher frequencies will spread out less, yielding a sharper difraction-peak. Also, a more narrow slit will yield a wave that is spread out more. This relation should make you think about the Heisenberg Uncertainty principle, right ?

    Last edited: Aug 17, 2005
  6. Aug 17, 2005 #5

    Andrew Mason

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    The extent to which the index of refraction depends on frequency varies with different media. But blue light will travel slower through the film than red, so it will bend more than red. So blue light is deflected farthest from the original path.

    Because the effective speed of blue light through the film is slower than red.

  7. Aug 17, 2005 #6
    so you're saying the answer is wrong because blue and red are not deflected the same amount?

    also, how do i find the speed of the electromagnetic waves through another media if i don't know it's n? or how can i use frequency of that wave to find the speed as it travels through another medium?
  8. Aug 18, 2005 #7

    Andrew Mason

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    That is generally correct. But it depends on the medium.

    There is no theoretical way to determine it. You just have to measure it. It depends on the medium.

  9. Aug 19, 2005 #8
    so in a way, is dispersion and refraction the same because they both deal with the refraction of light in different mediums?
    Last edited: Aug 19, 2005
  10. Aug 19, 2005 #9

    Andrew Mason

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    They are certainly related, but are slightly different concepts. Refraction is the change in direction of a light 'beam' (due to passing through a surface of a different medium at an oblique angle) whereas dispersion is the spreading out of different wavelengths of light due to different 'colors' of light having different indices of refraction at that surface (ie. and therefore bending at different angles when encounting the refracting medium).

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