![]() ![]() If the geometry is such that the small angle approximation is valid, the width of the pattern is inversely proportional to the slit width. The sketches of the slit widths at right were scaled to the difference between the first minima of the diffraction patterns. These single slit diffraction patterns were photographed with a helium-neon laser as the light source and a micrometer-controlled single slit. Single Slit Diffraction for Different Slit Widths Note: To obtain the expression for the displacement y above, the small angle approximation was used. The pattern below was made with a green laser pointer. The diffraction pattern at the right is taken with a helium-neon laser and a narrow single slit. If the conditions for Fraunhofer diffraction are not met, it is necessary to use the Fresnel diffraction approach. But an additional requirement is D> a 2/λ which arises from the Rayleigh criterion as applied to a single slit. Since you now understand the geometrical shift of the minimum along with a, you can make sense of this condition optically: If a phase shift of $\lambda/2$ results in a destructive interference, then shifting that phase by a whole $\lambda$ should again result in a destructive interference.Fraunhofer Diffraction Fraunhofer Diffraction GeometryĪlthough the formal Fraunhofer diffraction requirement is that of an infinite screen distance, usually reasonable diffraction results are obtained if the screen distance D > a. places with complete destructive interference. This is the condition for all minima in the intensity pattern, i.e. $xdist=a*sin(\theta)=m*\lambda$ (where m is a non-zero positive integer) In fact, you will notice that this works with all multiples of 2, so let's make the algebraic: Turns out this is the condition for the second minimum. If we use the diagram from the video you posted, the a/4 condition would mean that we have the distance of $xdist=\lambda/2$ higher up and therefore the angle of the resulting beam would be angled higher. What is the difference between a/2 and a/4: Think about it geometrically first. That leaves us with 1 entire section that does not destructively interfere, no minimum. ![]() ![]() Same thing with quadrant 2 and 4, hence we also have a minimum here.įor a/5 it does not work: We split the beam up into 5 sections, with 4 of them we can make the same argumentation as before. quadrant 1 and 3 destructively interfere. Beam 1 from quadrant 1 would destructively interfere with beam 1 from quadrant 3, etc. Figure 4.2.2 shows a single-slit diffraction pattern. Every beam in the top half would find a beam corresponding in the bottom half that would lead to destructively interference.įor a/4 we have the same case: We can split the beam up into 4 quadrants each containing an arbitrary number of beams. Diffraction through a Single Slit Light passing through a single slit forms a diffraction pattern somewhat different from those formed by double slits or diffraction gratings, which we discussed in the chapter on interference. Think about it this way: The a/2 condition essentially says that if you were to divide the beam up into two halves with an equally arbitrary resolution of beams in each half, then the first beam of the top half (at 0 measuring from the top of the slit) would destructively interfere with the first beam of the second half (at a/2 measuring from the top of the slit). ![]() This how is the variation in intensity is explained. When $xdist$ does not equal $a/2$, then you cannot do this 'pairing up' and some portion of the beam will not destructively interfere. That must be the case for some angle of the diffraction, and when that is the case you can 'pair' up a portion of the beam with another portion of the beam and you will get complete diffraction. The fact that $xdist = a/2$ is a condition not an assumption. ![]()
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