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I was looking at previous exams and I saw a question with single slit diffraction. Please look at picture on the website: http://www.physicsforums.com/showthread.php?p=4807732#post4807732

So, this made me think: "Wow, I never thought single slit diffraction could be applied in 2D with one pattern horizontal and the other vertical."

Then, I thought why is there no diffraction patterns along all the surface of the viewing screen. Can anyone explain why? The textbook I am using emphasizes how when a wave enters a boundary place, each point sends out its own spherical wavelet in 3D. So, why don't we see that on the viewing screen?

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  • $\begingroup$ Could you specify your question? Do you want to know why you cannot see "3D interference" on a two dimensional screen? Would your question be answered by moving the screen back and forth and thus capturing the depth of the interference pattern? $\endgroup$ – M.Herzkamp Jul 28 '14 at 10:36
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The off-axis intensity is not sero, it is simply quite low. This article on the Wolfram web site shows the 2D diffraction pattern from the sort of aperture you describe along with the equation for calculating the intensity:

$$ I = 16C^2a^2b^2\left(\frac{\sin(\theta_xka)}{\theta_xka}\right)^2\left(\frac{\sin(\theta_yka)}{\theta_yka}\right)^2 $$

where the width of the slit is $2a$ and the height $2b$.

The first maximum in $\text{sinc}^2(x)$ has an amplitude of about $0.047$, so the relative intensity of the first order spots in the $x$ and $y$ directions, $I_{10}$ and $I_{01}$, will be $4.7$% of the central spot. However the intensity of the first off axis spot, $I_{11}$, will be $0.047^2$ or about $0.2$% of the central spot, which is so faint it's hard to see. Higher order off-axis spots are even fainter.

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  • $\begingroup$ So, for a rectangular single slit, I would observe an off-axis intensity that is not zero? Sorry for sounding redundant, but the website you linked mentions the "Franhaufer" diffraction. I am not sure if it only applies to that type of aperture. $\endgroup$ – yolo123 Jul 28 '14 at 11:41
  • $\begingroup$ @user154734: yes. Fraunhofer diffraction is just the limit in which the size of the aperture is small compared to the distance between the aperture and the screen showing the diffraction pattern. $\endgroup$ – John Rennie Jul 28 '14 at 11:46

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