Solving for Slit Width-Wavelength Ratio at $\pm90°$ Diffraction Pattern

In summary: Double check the angle on the |n| = 1 interpretation I gave you. I might have screwed up left and right. But in the long run, no, it doesn't really matter.
  • #1
MermaidWonders
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0
For what ratio of slit width to wavelength will the first minima of a single-slit diffraction pattern occur at $\pm 90°$?

The thing is, when I did it, I used the formula $sin\theta = \frac{n\lambda}{a}$, and used the fact that $m = 1$ and $\pm 90°$ to solve for $\frac{a}{\lambda}$. However, I don't know if we're supposed to plug in $-90°$ for $sin\theta$, because that would mean that our ratio of $\frac{n\lambda}{a}$ would be $-1$ as opposed to just $1$ (when $sin90°$ was plugged in)...
 
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  • #2
MermaidWonders said:
For what ratio of slit width to wavelength will the first minima of a single-slit diffraction pattern occur at $\pm 90°$?

The thing is, when I did it, I used the formula $sin\theta = \frac{n\lambda}{a}$, and used the fact that $m = 1$ and $\pm 90°$ to solve for $\frac{a}{\lambda}$. However, I don't know if we're supposed to plug in $-90°$ for $sin\theta$, because that would mean that our ratio of $\frac{n\lambda}{a}$ would be $-1$ as opposed to just $1$ (when $sin90°$ was plugged in)...
More or less we can take the sign of \(\displaystyle sin( \theta )\) to be "attached" to the n. A positive n describes the nth minima to the right of the central maximum and a negative n describes the nth minima to the left of the central maximum.

-Dan
 
  • #3
topsquark said:
More or less we can take the sign of \(\displaystyle sin( \theta )\) to be "attached" to the n. A positive n describes the nth minima to the right of the central maximum and a negative n describes the nth minima to the left of the central maximum.

-Dan

OK, makes sense. So should I take the absolute value, since a negative ratio wouldn't be very meaningful in this context?
 
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  • #4
MermaidWonders said:
OK, makes sense. So should I take the absolute value, since a negative ratio wouldn't be very meaningful in this context?
Yup.

Double check the angle on the |n| = 1 interpretation I gave you. I might have screwed up left and right. But in the long run, no, it doesn't really matter.

-Dan
 
  • #5
Yeah, OK, makes sense. Thanks so much!
 

Related to Solving for Slit Width-Wavelength Ratio at $\pm90°$ Diffraction Pattern

What is the significance of solving for slit width-wavelength ratio at ±90° diffraction pattern?

The slit width-wavelength ratio at ±90° diffraction pattern is an important factor in diffraction experiments. It helps determine the diffraction pattern that will be produced and provides information about the size of the slit and the wavelength of the incident light.

How is the slit width-wavelength ratio at ±90° diffraction pattern calculated?

The slit width-wavelength ratio at ±90° diffraction pattern can be calculated using the formula:
w/λ = (nλ)/(sinθ), where w is the width of the slit, λ is the wavelength of the incident light, n is the order of diffraction, and θ is the angle of diffraction.

What is the ideal slit width-wavelength ratio for producing a clear diffraction pattern?

The ideal slit width-wavelength ratio for producing a clear diffraction pattern is when the value is close to 1. This indicates that the slit width is similar to the wavelength of the incident light, allowing for a well-defined diffraction pattern.

How does the slit width-wavelength ratio affect the diffraction pattern?

The slit width-wavelength ratio directly affects the diffraction pattern. A smaller ratio will result in a wider diffraction pattern, while a larger ratio will produce a narrower pattern. This is due to the diffraction of light waves passing through the slit.

What are the practical applications of solving for slit width-wavelength ratio at ±90° diffraction pattern?

The calculation of slit width-wavelength ratio at ±90° diffraction pattern is useful in various fields such as optics, spectroscopy, and crystallography. It can also be used to determine the wavelength of light in experiments and to analyze the properties of materials based on their diffraction patterns.

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