How does a CD act like a diffraction grating?

[Jimmy87]

Hi, I having been looking on the internet and other threads and can't seem to find any detailed information on how a CD acts like a diffraction grating.

What I understand: the CD has lots of little bumps which can split up light into its various colors. These colors can interfere constructively or destructively which gives the diffraction pattern.

What I don't understand: the mechanism for why the light splits up. Why does white light simply hitting little bumps split the light up? For example, say you have the white light hitting a particular part of the bump why does this cause the colors split? Finally, why is this diffraction? I thought diffraction was the spreading out of waves which is why it is used to explain the fact we can hear sounds going around corners. I don't see how colors of light bouncing off at different angles from a CD has any similarity to what I have read diffraction to be?

Many thanks for anyone who has time to help!

 

[Drakkith]

Per wiki: Diffraction refers to various phenomena which occur when a wave encounters an obstacle or a slit. In classical physics, the diffraction phenomenon is described as the interference of waves according the Huygens Fresnel principle

The bumps on a CD count as "obstacles" in the sense that they cause part of the EM wave to reflect at a different angle. When this happens the wave interferes with itself, causing it to constructively and destructively interfere in different directions. The direction that it constructively interferes with itself is the direction that it reflects at. Since the color of light depends on the wavelength, different colors are reflected in different directions.

 

[Soylent Grin]

"I thought diffraction was the spreading out of waves..."

I have a thought experiment that might help.
Imagine holding a bunch of rubber bb's and dropping them on a flat floor. They'll bound back upward, and scatter a little.
Now, imagine dropping a stream of them on a bump, like the "turtles" that act as lane separators on a road. Or an overturned soup bowl. What kind of scatter, or spreading out, will happen now?

 

[Jimmy87]

Per wiki: Diffraction refers to various phenomena which occur when a wave encounters an obstacle or a slit. In classical physics, the diffraction phenomenon is described as the interference of waves according the Huygens Fresnel principle

The bumps on a CD count as "obstacles" in the sense that they cause part of the EM wave to reflect at a different angle. When this happens the wave interferes with itself, causing it to constructively and destructively interfere in different directions. The direction that it constructively interferes with itself is the direction that it reflects at. Since the color of light depends on the wavelength, different colors are reflected in different directions.

Thank you for the answers. So if I understand the mechanism correct - if you have different colors striking a bump at a particular angle then the different colors will scatter off at DIFFERENT angles and it is their difference in WAVELENGTH that causes this? Have I understood you correctly?

 

[Jimmy87]

Per wiki: Diffraction refers to various phenomena which occur when a wave encounters an obstacle or a slit. In classical physics, the diffraction phenomenon is described as the interference of waves according the Huygens Fresnel principle

So saying that diffraction is the spreading out of a wave is not a true definition? Or can you describe a diffraction grating as the spreading out of a wave?

 

[jtbell]

Natural language is not always logical. If it were up to me, I would rename "diffraction gratings" to "interference gratings." But I'm not the Tsar of Physics Terminology.

(And I'd abolish the term "rest mass" in relativity, in favor of "invariant mass"... but that's a subject for another thread. )

 

[Drakkith]

Thank you for the answers. So if I understand the mechanism correct - if you have different colors striking a bump at a particular angle then the different colors will scatter off at DIFFERENT angles and it is their difference in WAVELENGTH that causes this? Have I understood you correctly?

Yes, as long as the bump is of comparable size to the wavelength. If the bump is much smaller than the wavelength then only a small part of the wavefront will be reflected at a different angle. The interference effect is directly related to how much of the wavefront is reflected at different angles, so when only a small part of the wavefront is reflected away from the main wavefront, the interference effect is very small, too small to cause a noticeable change in the angle that the wavefront as a whole is reflected at.

If you have too large of a bump, the wavefront sees it as a close approximation of a flat surface and it simply reflects accordingly. Think of a curved telescope mirror that is 10 inches in diameter. The wavelength of visible light is between 700 and 450 nm, so the mirror is MUCH larger than the wavelength of visible light. Because of this, any small section of the wavefront sees the mirror as very nearly flat, similar to how you and I see the surface of the Earth as very nearly flat, and reflects as if it were a flat surface.

So saying that diffraction is the spreading out of a wave is not a true definition? Or can you describe a diffraction grating as the spreading out of a wave?

I'd say that diffraction is the way a wavefront changes in how it propagates after encountering an obstacle or obstruction. So it is propagating in one way before the obstruction, and afterwards it is propagating differently. This change is diffraction, and it is modeled by the Huygens Fresnel Principle.

According to the Huygens Fresnel Principle each point on an emitting surface can be modeled as an emitter of a spherical wave, and it the sum of all these emitted waves interfering with each other that determines how the wavefront propagates. When something obstructs the wavefront or emits waves that add with the wavefront, interference between these waves causes the wavefront to change.

So the spreading out of a wave after it encounters an obstruction can be said to be caused by diffraction.

 

[dauto]

The bumps don't separate the colors. All colors scatter in all directions. The scattered waves coming from those bumps interfere with each other. At places there is constructive interference producing brighter light. At other places the interference is destructive producing dimmer light. So the light seems to scatter in a specific direction. Since the direction is dictated by the interference pattern and interference depends on wavelength (color), the colors separate from each other.

 

[UltrafastPED]

Here is a lesson plus how-to for CD base diffraction gratings:
http://www.nnin.org/sites/default/f...NG_CDs_AND_DVDs_AS_DIFFRACTION_GRATINGS_0.pdf

 

[Jimmy87]

According to the Huygens Fresnel Principle each point on an emitting surface can be modeled as an emitter of a spherical wave, and it the sum of all these emitted waves interfering with each other that determines how the wavefront propagates. When something obstructs the wavefront or emits waves that add with the wavefront, interference between these waves causes the wavefront to change.

So the spreading out of a wave after it encounters an obstruction can be said to be caused by diffraction.[/QUOTE]

Thanks to all for the answers, very helpful. That Huygens Fresnal Principle interests me. I recently watched an MIT lecture from Walter Lewin where he said this was a classical explanation for the reason being that emitters of new spherical wavefronts do not fit with the idea that new sources of EM wavefronts would require accelerated charges to generate new EM waves. So, he said that there is an alternative quantum explanation but says it beyond the scope of the lecture. Could you briefly explain (or point me to a good book/reference) for the quantum explanation he is referring to which replaces this classical notion that the emitting surface produces new point sources of spherical waves?

 

[UltrafastPED]

Could you briefly explain (or point me to a good book/reference) for the quantum explanation he is referring to which replaces this classical notion that the emitting surface produces new point sources of spherical waves?

See Richard Feynman's four lectures on "QED: The Strange Theory of Light and Matter"; also available as a book, which is suitable for reading multiple times during your studies of physics - at each level more will click!

http://vega.org.uk/video/subseries/8

Note: there are four lectures; each takes about 75 minutes, so like the audience, take it in four sittings!