Homework Help: Most significant diffraction

1. May 20, 2013

songoku

1. The problem statement, all variables and given/known data
Which electromagnetic wave would cause the most significant diffraction effect for grating diffraction?
a. infra red (10-5 m)
b. micro wave (10-2 m)
c. ultraviolet (10-8m)
d. X-ray (10-10m)

2. Relevant equations

3. The attempt at a solution
I know the most observable diffraction is when the wavelength is more or less the same as the gap width. So how can I know about the gap width? Gratings can have different gap width, depends on the number of lines per length.

I've tried several value of number of lines per length, such as 3500 lines / cm, 5000 lines / mm, etc and the closest answers are infra red and ultraviolet. My answer will be ultraviolet. Is there method or theory to determine the most significant diffraction?

Thanks

2. May 21, 2013

BruceW

hmm. they don't give the gap width, so I don't think you should try to estimate it. I agree that observable diffraction occurs when the wavelength is more or less the same as the gap width. but what happens when the wavelength is greater than the gap width? I think this is the key to the answer.

3. May 21, 2013

songoku

If the wavelength is greater than the gap width, the diffraction still occurs but the spreading of the wave will be less. I think the wave will be more focused on the center area of the screen.

So the answer is ultraviolet, because it has smaller wavelength than infra red? I am still not really sure.

Thanks

4. May 22, 2013

BruceW

I don't think that is right. why would the spreading of the wave be less for larger wavelengths?

5. May 22, 2013

ehild

There are gratings for IR, visible and UV, with different separation between slits (D). For visible, D is usually in the range 1-10 micrometer. You should know what kind of grating is meant by the problem.

The first maximum appears at angle θ where Dsinθ=λ. What happens if D<λ? Can you see a diffraction pattern? What happens if D>>λ?

ehild

6. May 22, 2013

technician

microwaves are 10^-6m not 10^-2m

7. May 22, 2013

ehild

That is not true. 10-6m is 1 micrometer, it is in the near infrared range of the electromagnetic spectrum. The wavelength of microwaves is in the m - mm range.

ehild

8. May 24, 2013

songoku

I am not sure, maybe because the wave will be more difficult passing through the small gap?

How we can know the grating meant by the problem? I can't see the hint from the question to direct me to know the type of grating used.

If D < λ, we can still see the diffraction pattern but the pattern will be more focused on the center of the screen because the wave is less spread.

If D >> λ, we can't see the clear pattern of diffraction because the wavefront only bends at the edge (only small portion of the wavefront bends).

"For visible, D is usually in the range 1-10 micrometer." So this means D is in range of 10-6 - 10-5. The answer should be infra red.

Are my reasoning above correct? Thanks

9. May 25, 2013

BruceW

where did you get that quote from? Are you meant to assume that the grating is visible by the human eye?

10. May 25, 2013

ehild

I do not understand what is meant on "grating diffraction" and "on most significant diffraction effect". When we speak about diffraction gratings they consist of parallel slits or groves at equidistant distance from each other. The light is diffracted by each slit and the diffracted waves interfere to produce a diffraction pattern with maxima and minima. A single slit the more diffracts the light wave the narrower the slit is with respect to the wavelength. The diffraction pattern of the grating, that is, the distance between maxima and minima depends on the distance between the slits. If the distance between the slits is less than the wavelength, you do not get the diffraction pattern. So the optimum distance between the slits depends on the wavelength range you want to use the grating for, but you get the most clear diffraction pattern if the slits are narrow with respect to the wavelength.

ehild

11. May 26, 2013

technician

Absolutely correct! Sorry....my mistake

12. May 27, 2013

songoku

Why can't we get diffraction pattern when the distance between the slits is less than wavelength?

What happen if the distance between slits is larger than wavelength? I thought this is the case in which we can't get diffraction pattern.

Thanks

13. May 28, 2013

ehild

The incoming light diffracts at each slit. The diffraction is most effective if the slit is narrow. Narrow slits act as line sources of light according to Huygens' principle, and the wavefronts look as concentric arcs as shown in the picture. That is the same as if light rays would travel in every direction after leaving the slits. Rays travelling in the same direction θ will combine to a single plane wave far from the grating, with intensity governed by the path difference between the rays. The path difference is Dsinθ if the slits are separated by distance D. If the path difference is half the wavelength we get the first minimum, Dsin θ =λ/2 and the other minima are at angles D sinθ =(2k+1)λ/2, where the diffracted rays cancel each other. If Dsinθ =λ we get the first bright image of the slit, on both sides of the central maximum.. If D<λ, sinθ=λ/D>1, the first bright image can not appear. We might get some pattern from the waves emerging from the second, third .... slits, but that pattern would be blurred.

If the distance between the slits is larger than the wavelength we get maxima at angles Dsinθ =kλ. The bright lines get closer and closer if D increases with respect to the wavelength, till they get closer than their width, or the path difference exceeds the coherence length of the light: we do not see diffraction pattern.

ehild

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14. Jun 2, 2013

songoku

Thanks a lot for the explanation