繞射光柵干涉的產生需要相干波源嗎？

Atheist

2012-02-15 9:39 pm

For interference to occur using double slit, waves packets from a light source must be coherent. But how about for that using diffraction grating?

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/grating.html#c1

It states that:
The hydrogen gas in a thin glass tube is excited by an electrical discharge and the spectrum can be viewed through the grating.
and
The tracks of a compact disc act as a diffraction grating, producing a separation of the colors of white light.

But I am confused because I don't see the above situations can give coherent light source.

回答 (1)

天同

2012-02-21 11:31 pm

✔ 最佳答案

You are right that coherent light is necessary for a stable interference pattern to occur.

But in the case of diffraction grating, you should recall that the path difference between two slits is about [a.sin(theta)], where a is the slit separation and angle(theta) is the angular positions of bright fringes. A grating generally has value of a in oder of micrometer (10^-6 m). Since sin(theta) has values always smaller than one. The path difference [a.sin(theta)] is around 1 um in general.

Spectral light (e.g. the hydrogen spectral light) can have "coherence lenght" (it represents the degree of phase stability of a wave) of about tens of cm, which is much longer than white light. As the path difference in a diffraction grating (order of 1 um) is much shorter than the coherence length, stable interference pattern could be achieved.

For similar reason, the CD shown has a slit separation of about 1.6 um, which is comparable to the coherence length of white light (also about 1 um). Hence, you could observe the interference pattern.

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