Maximum Width of Single Slit for No Diffraction Minima?

In summary, to find the maximum Width (D) of a single slit with no diffraction minima, you can use the formula D * sin (\theta) = m \alpha and take into consideration the sine function and the geometry of the setup. This results in D being equal to the wavelength \alpha.
  • #1
leolaw
85
1
Given a wavelength length [tex]\alpha[/tex], what is the maximum Width (D) of a single slit, which would have no diffraction minima?

It seems like a proof problem to me and I am trying to get a head start.
should I use [tex] D * sin (\theta) = m \alpha[/tex] ?
 
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  • #2
leolaw said:
Given a wavelength length [tex]\alpha[/tex], what is the maximum Width (D) of a single slit, which would have no diffraction minima?

It seems like a proof problem to me and I am trying to get a head start.
should I use [tex] D * sin (\theta) = m \alpha[/tex] ?

Yes, that and what you know about the sine function.
 
  • #3
that sin of zero degrees is 0
 
  • #4
leolaw said:
that sin of zero degrees is 0

Yes, but at zero degrees you will never have a minimum. From the geometry of the single slit diffraction setup, to not find any minima after the slit, the angle [itex] \theta [/itex] would have to be 90 degrees for the first minimum. So then what does

[tex] D * sin (\theta) = m \alpha[/tex]

tell you about D?
 
  • #5
I see, so [tex]D sin (90) = (1) \alpha[/tex], which is the first minimum, and D has to be equal to the wavelength [tex]\alpha[/tex].
 

1. What is the wave-particle duality of light?

The wave-particle duality of light is the concept that light exhibits both wave-like and particle-like behavior. This means that light can act as a wave with properties such as interference and diffraction, but also as a particle with properties such as energy and momentum.

2. What is the difference between a wave and a particle?

A wave is an oscillation that carries energy through a medium, while a particle is a localized unit of matter with mass and other properties. In the case of light, it can behave as a wave or a particle depending on the experimental setup.

3. How does the wave nature of light explain phenomena like diffraction and interference?

The wave nature of light explains diffraction and interference by treating light as an electromagnetic wave. When light passes through a narrow slit or encounters an obstacle, it diffracts, or bends, around the edges. This results in an interference pattern, where the diffracted waves interact and produce areas of constructive and destructive interference.

4. Can light be both a wave and a particle at the same time?

Yes, light can exhibit both wave and particle behavior at the same time, but the two aspects cannot be observed simultaneously. This is known as the wave-particle duality and is a fundamental concept in quantum mechanics.

5. How does the wave nature of light affect its speed?

The wave nature of light affects its speed by determining the refractive index of a medium. The refractive index is a measure of how much light is slowed down when it passes through a material. Light travels fastest in a vacuum where it behaves purely as a wave, but its speed decreases when it passes through materials due to interactions with particles in the medium.

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