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.

 

[mezarashi]

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

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

which is derived geometrically.

 

[Doc Al]

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]

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.