Maximum Slit width diffraction minima

In summary, the maximum slit width for no visible light to exhibit a diffraction minimum is when the slit width is equal to the wavelength of light passing through it. For visible light with wavelengths ranging from 400 nm to 750 nm, the maximum slit width would be 400 nm. This is because when the slit width is smaller than the wavelength, there will be no diffraction minimum.
  • #1
Decelerate
5
0

Homework Statement



What is the maximum slit width so that no visible light exhibits a diffraction minimum?(Visible light has wavelengths from 400 nm to 750 nm.)


Homework Equations



D*sin(theta)=m*lambda ; where D = slit width,theta in degrees, m =1,2,3,..., and lambda is wavelength. The maximum slit width occurs at sin(90) =1 and if we take m=1 the equation reduces to D=lambda. When the slit width is equal to the wavelength of light passing through it then no diffraction minima are observed.

The Attempt at a Solution



For visible light, I just assumed that the maximum slit width had to be equal to the largest wavelength contained in visible light (750nm), but this does not make sense because then the wavelength at 450nm would still be defracted. I know for a fact that a slit width of 750nm is wrong, so I am guessing that the answer might be 450nm or maybe the average wavelength of visible light but am not sure

Any help is greatly appreciated.
 
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  • #2
Minimum intensity occurs at [tex] \sin\theta_{min} = \frac{\lambda}{d} [/tex] .

So when is there no [tex] \theta_{min}[/tex]?
 
  • #3
I guess my question is what wavelength do you use for visible light? It is a mixture of different wavelengths so How do I determine D when there are multiple wavelengths of light is it just the smallest wavelength (400) or the average...?
 
  • #4
Decelerate said:
I guess my question is what wavelength do you use for visible light? It is a mixture of different wavelengths so How do I determine D when there are multiple wavelengths of light is it just the smallest wavelength (400) or the average...?

When does [tex] \theta_{min} [/tex] not exist?
 
  • #5
zachzach said:
When does [tex] \theta_{min} [/tex] not exist?

When lambda is larger than d...I still don't really understand how that will help me determine the width for visible light from 400-750
 
  • #6
Decelerate said:
When lambda is larger than d...I still don't really understand how that will help me determine the width for visible light from 400-750

So when [tex] d < \lambda , \theta_{min} [/tex] DNE. So if [tex] d = 700nm [/tex] what range does not have a minimum? What about if [tex] d = 600nm [/tex]?
 
  • #7
I had to edit that fyi.
 
  • #8
so i guess d has to be 400nm for the range of 400-750 to not have a minimum
 
  • #9
Decelerate said:
so i guess d has to be 400nm for the range of 400-750 to not have a minimum

That is my guess as well, less than 400nm but yeah.
 
  • #10
Let me enter it in and see if it is right.
EDIT: yes 400nm is right
Thanks!
 

1. What is the concept of maximum slit width diffraction minima?

The concept of maximum slit width diffraction minima refers to the phenomenon of light diffraction that occurs when a beam of light passes through a narrow slit. This results in the formation of a diffraction pattern, where the maximum intensity of light is observed at the center of the pattern, but decreases as the distance from the center increases.

2. How is the maximum slit width diffraction minima calculated?

The maximum slit width diffraction minima is calculated using the formula d*sinθ = m*λ, where d is the slit width, θ is the angle of diffraction, m is the order of diffraction, and λ is the wavelength of light. This formula is known as the grating equation and is used to determine the location of the diffraction minima.

3. What factors affect the maximum slit width diffraction minima?

The maximum slit width diffraction minima is affected by several factors, such as the wavelength of light, the slit width, the distance between the slit and the screen, and the angle of diffraction. These factors can alter the intensity and location of the diffraction minima, resulting in a different diffraction pattern.

4. How does the number of slits in a diffraction grating affect the maximum slit width diffraction minima?

The number of slits in a diffraction grating has a significant impact on the maximum slit width diffraction minima. As the number of slits increases, the diffraction pattern becomes more defined and the maximum intensity of the diffraction minima increases. This is because more slits allow for more light to pass through, resulting in a stronger diffraction pattern.

5. What are some real-world applications of maximum slit width diffraction minima?

The concept of maximum slit width diffraction minima has various applications in the fields of optics and spectroscopy. It is used in the design of diffraction gratings, which are used in spectrometers to separate light into its different wavelengths and analyze the composition of a substance. It is also used in the study of wave properties of light and in the development of optical devices such as cameras and telescopes.

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