Single-slit diffraction and wavelength

In summary: I've been seeing this incorrect information for years and years, and I never knew how to correct it.In summary, the diffraction equation states that asin(theta) = m(lamda), meaning that a minimum will never occur when the wavelength is greater than the width of the slit.
  • #1
proton
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I keep hearing that single-slit diffraction only occurs when the magnitude of the wavelength of the wave is larger than the slit. But according to the diffraction equation asin(theta) = m(lamda), minima can never occur when the wavelength is greater than the slit. I've tried reading my textbook many times, looking at online articles on diffraction, but none seem to answer my question. Could someone please help me on this?
 
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  • #2
proton said:
I keep hearing that single-slit diffraction only occurs when the magnitude of the wavelength of the wave is larger than the slit.

That is simply not correct. I hope you're not seeing this in a real physics textbook. Sloppily written popular presentations and Web sites, on the other hand...

But according to the diffraction equation asin(theta) = m(lamda), minima can never occur when the wavelength is greater than the slit.

That is correct. When the wavelength equals the width of the slit, the first minimum occurs at 90 degrees, that is, the entire "field of view" in front of the slit is filled by the central peak of the diffraction pattern. When the wavelength is longer, the "sides" of the central peak get chopped off at the 90-degree point on both sides, but the intensity still has a maximum at the center and decreases as theta increases in either direction.
 
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  • #3
this is from wikipedia: "The most conceptually simple example of diffraction is single-slit diffraction in which the slit is narrow, that is, significantly smaller than a wavelength of the wave."
 
  • #4
can someone please help?
 
  • #5
proton said:
this is from wikipedia: "The most conceptually simple example of diffraction is single-slit diffraction in which the slit is narrow, that is, significantly smaller than a wavelength of the wave."
The diffraction from a slit that is less than a wavelength does not exhibit the interference pattern you see from a wider slit. Look at the picture at Wikipedia. There are no minima, just circular waves leaving the slit. Diffraction is still ocurring, i.e., the barrier around the slit does not create a shadow.

An ideal double slit experiment would use slits that are less than a wavelength to get semicircular waves from the slits. Then the observed interference pattern would be purely double slit interference.
 
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  • #6
You're interested in diffraction, rather than interference? Diffraction will occur regardless of the relation between slit width and wavelength, it is the effect whereby light doesn't all go in quite a straight line. A narrow slit experiment is an extreme example where, though you would expect the light to shine only in one precise direction, it is actually visible from almost every direction. You can see another example in your shadow if you slowly move two fingers very close to each other. Your equation seems to be for interference, the effect whereby light originating from different positions (ie. along a not-quite-so-narrow slit) overlaps to enhance or cancel out in different directions.
 
  • #7
In fact, if you remove one side of the slit completely, leaving only one edge and producing a "slit" that is (semi-)infinitely wide, you still get diffraction around the remaining edge. This is often called "knife edge diffraction".
 
  • #8
jtbell said:
In fact, if you remove one side of the slit completely, leaving only one edge and producing a "slit" that is (semi-)infinitely wide, you still get diffraction around the remaining edge. This is often called "knife edge diffraction".
Which is also a problem with any telescope where a secondary mirror is held by "spider vanes" crossing the field of incoming light to the main objective. Even a secondary without vanes, as in an SCT or Maksutov, causes diffraction from the edges of the secondary simply because it (the secondary) is there.

With vanes, you get the famous "difraction spikes" seen in so many photos. With just a secondary you get diffraction "smear" where all wavelengths are scattered across the whole image which lowers both contrast and resolution. The best view, and photos, you see come from refractors where all the objects, especially stars, are sharp and pinpoint.

Off subject, I know, but I couldn't resist...:biggrin:
 
  • #9
cesiumfrog said:
Your equation seems to be for interference, the effect whereby light originating from different positions (ie. along a not-quite-so-narrow slit) overlaps to enhance or cancel out in different directions.

So if I'm understanding you correctly, the asin(theta) = m(lamda) for minima in diffraction where 'a' is the width of the slit is used only whenever interference ALSO occurs in the diffraction of light from the sinlge-slit? If so, then I've been wasting so much time reading the textbook over and over just for some slight misinterpretation of the text!

I greatly thank everyone for their help!
 

Related to Single-slit diffraction and wavelength

1. What is single-slit diffraction?

Single-slit diffraction is a phenomenon in which a single slit is placed in front of a light source, causing the light waves to spread out and interfere with each other, creating a diffraction pattern.

2. How does the width of the slit affect single-slit diffraction?

The width of the slit affects the diffraction pattern by determining the amount of diffraction that occurs. A wider slit will result in a narrower diffraction pattern, while a narrower slit will result in a wider diffraction pattern.

3. What is the relationship between wavelength and single-slit diffraction?

The relationship between wavelength and single-slit diffraction is that as the wavelength of light decreases, the amount of diffraction increases. This means that shorter wavelengths, such as blue light, will create a wider diffraction pattern compared to longer wavelengths, such as red light.

4. How is single-slit diffraction used in everyday life?

Single-slit diffraction is used in many everyday devices, such as CD players, DVD players, and laser pointers. It is also used in diffraction gratings, which are used in spectrometers to analyze the wavelength of light.

5. What is the difference between single-slit diffraction and double-slit diffraction?

The main difference between single-slit diffraction and double-slit diffraction is the number of slits used. Single-slit diffraction involves only one slit, while double-slit diffraction involves two slits. This results in different diffraction patterns, with double-slit diffraction producing a more complex interference pattern.

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