How Many Interference Maxima Appear Within the Central Diffraction Peak?

In summary, the question is asking how many interference maxima lie within the central diffraction peak when light with a wavelength of 530 nm is incident on two slits spaced 1.0 mm apart, each with a width of 0.1 mm. The answer is 21, which can be found by calculating the halfwidth of the diffraction pattern (0.304°) and using the formula for the maxima of the interference pattern.
  • #1
akmphy
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Homework Statement


Light with a wavelength of 530 nm is incident on 2 slits that are spaced 1.0mm apart. If each slit has a width of .1mm, how many interference maxima lie within the central diffraction peak?

Homework Equations



sin( degree) = m(lambda)/d

The Attempt at a Solution


I have no idea what the question is asking, but I started with:

arc sin ( 1 * 530e-9)/ .001
I got .03 degrees for the half width of the central diffraction.
Double this degree, .06, for the entire width of the central diffraction.

I then did:
[sin(.06) * .001]/530e-9 = m
m = 1.97

So wrong! The answer is 21.
Please help me understand this.
Thanks.
 
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  • #2
The halfwidth of the diffraction pattern is about lambda/width of the slit, so it is 0.304°.
The maxima of the interference pattern of the two slits are apart by lambda/(distance between the slits).

ehild
 
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FAQ: How Many Interference Maxima Appear Within the Central Diffraction Peak?

1. What is interference maxima and why is it important in science?

Interference maxima is a phenomenon that occurs when two or more waves overlap and create areas of high amplitude or intensity. It is important in science because it helps us understand how waves interact and how they can be manipulated for various applications.

2. How does interference maxima differ from interference minima?

Interference maxima occurs when the crests of two waves align, resulting in a higher amplitude, while interference minima occurs when the crests of one wave align with the troughs of another, resulting in a lower amplitude. In other words, interference maxima is a point of constructive interference, while interference minima is a point of destructive interference.

3. What factors affect the formation of interference maxima?

The factors that affect the formation of interference maxima include the wavelength, amplitude, and phase difference of the waves, as well as the distance between the sources of the waves. These factors can either enhance or cancel out the interference, resulting in different patterns of maxima and minima.

4. How is interference maxima used in real-life applications?

Interference maxima is used in various real-life applications, such as in the field of optics for creating diffraction grating patterns, in music for producing beats and harmonies, and in radio technology for producing stronger signals. It is also utilized in scientific experiments to study the properties of waves and their behavior.

5. Can interference maxima occur with other types of waves besides light waves?

Yes, interference maxima can occur with other types of waves, such as sound waves, water waves, and electromagnetic waves. As long as two or more waves overlap and interfere with each other, interference maxima can be observed. The principles of interference are applicable to all types of waves.

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