Single slit diffraction maxima

ruku320

Hi, I was wondering if anyone could help me with this problem.

Calculate the distance y between adjacent maxima in single slit diffraction patterns. Your answer should be given in terms of a, λ and D. (a is the length of the slit, D is the distance between the slit and the screen and λ is the wavelength of the light).

Ok, so I know how to get the minima of single slit diffraction. You just break it down into many rays going through the slit to get a*sin O=nλ. So is it just the same for the maxima? Say for two rays you would get (a/2)*sin O=nλ (nλ since you want the two rays to constructively interfere and when its nλ they are perfectly in phase) so in general it would be be a*sin O = 2nλ. This doesn't really make much sense though...cause the 2nλ distances are just multiples of nλ which is the minima.

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mezarashi

Homework Helper
For a single slit experiment, the condition for constructive interference is:

$$dsin\theta = (n + \frac{1}{2})\lambda$$

which is derived geometrically.

Doc Al

Mentor
While it's easy to find the minima for the single slit diffraction pattern, there's no simple formula for the maxima. The positions of the minima are given by:
$$dsin\theta = n\lambda$$

The maxima are not found exactly in the middle between the minima. See here for details: http://scienceworld.wolfram.com/physics/FraunhoferDiffractionSingleSlit.html

(Depending upon the level of the course, they may want you to use mezarashi's formula as a rough approximation, but realize that this is not really correct.)

McLaren Rulez

Hi everyone. Could anyone please explain why there is no simple argument to understand where the maxima of a single slit diffraction pattern are found? Why doesn't the same argument as for the minima work? I'm a freshman in university btw so you know what level of education I have.Thanks!

tuhinsiddik

Re: Single slit diffraction

Hi,I have been facing some problem in single slit diffraction and need precise description.

we know from single slit diffraction,in term of destructive interfere a sinθ=nλ and constructive
interfere a sinθ=(2n+1)λ/2.Here (a is the length of the slit, D is the distance between the slit and the screen and λ is the wavelength of the light and θ is the diffraction angle).

But we know from the constructive interference in term of sound or light, path difference=nλ (even multiples of λ) and in case of destructive interference,path difference=(2n+1)λ/2(uneven multiples of λ) .

Could anybody describe thoroughly, in term of single slit diffraction,why the condition of constructive and destructive interference place opposite to each other. Please anyone solve my problem.

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