Diffraction grating (missing diffraction beam)

In summary, the diffraction grating has a slit width of 0.83 μm, and when light of 430 nanometres is used, diffracted beams are observed at 14 degrees 55 minutes and at 50 degrees 40 minutes to the zero order. The first beam is assumed to be the first order and the other one can be calculated to be the third order. However, the second order is missing, likely due to the interference caused by the many slits in the grating. To calculate the angles of the diffracted beams, you use the given information to calculate the grating spacing, angle of diffraction for the second order, and angle of diffraction for the single-slit dark band. If you keep a constant
  • #1
pfellas
3
0

Homework Statement


A diffraction grating has slit width 0.83 micrometres. When light of 430 nanometres is used, diffracted beams are observed at 14 degrees 55 minutes and at 50 degrees 40 minutes to the zero order. The first beam is assumed to be the first order and the other one can be calculated to be the third order. Why is the second order missing?


Homework Equations


d Sin (theta) = n x Lamda

The Attempt at a Solution


I know that the slit width has something to do with this. Does the width of the slit cause a single slit effect which counteracts the diffraction effects for the 2nd order only but allows the first and third order to be visible?
 
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  • #2
Welcome to Physics Forums :smile:
pfellas said:
I know that the slit width has something to do with this. Does the width of the slit cause a single slit effect which counteracts the diffraction effects for the 2nd order only but allows the first and third order to be visible?
That could well be what is going on. [EDIT: see my post #5 below] [STRIKE]But to me it seems to be a weird setup, to have such a narrow slit combined with a diffraction grating. I have a hard time imagining how they are combined, is there any other information in the problem statement? Do they say or indicate if this is a transmission or reflection grating?[/STRIKE]

At any rate, you can use the given information to calculate:
  • The grating spacing
  • The angle of the 2nd-order diffracted beam
  • The angle of the single-slit dark band
Then you can compare those two angles, and see if they are equal.
 
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  • #3
In a diffraction grating, you can see the interference pattern due to double slit and diffraction pattern due to single slit. If a is the slit width, b is the spacing, then (a+b) will be the distance between the slits. If θ is the angle of diffraction of nth maximum due to interference, then we have
(a+b)sinθ = nλ.
If α is the angle of diffraction for pth minimum due to diffraction, then
a*sinα = πλ.
If you keep a constant and change b, the spacing between the interference maxima changes.
At a certain value of a and b, it is possible that , for the same value of θ, certain interference maximum may coincide with diffraction minima at the same position on the screen. when this happen, those maxima will not be visible and they are called the missing orders.
When a = b, second, fourth, sixth etc., orders of interference maxima are missing.
When 2a = b, third, sixth, ninth..etc., orders are missing.
 
  • #4
Thank you both very much! Much appreciated.
 
  • #5
You're welcome.

After reading rl.bhat's response, I realize now that the grating is made of many slits, each of the given 0.83 μm width, and to-be-determined spacing. So it's a transmission grating, not a reflection grating as I am used to seeing in practice.
 

1. What is a diffraction grating?

A diffraction grating is an optical element that is used to separate white light into its component colors, similar to a prism. It consists of a large number of parallel, equally spaced slits that cause light to diffract and produce an interference pattern.

2. Why is there a missing diffraction beam in a diffraction grating?

In a diffraction grating, the slits are very close together and the light is diffracted at different angles. This causes the diffraction pattern to be spread out, with some of the beams overlapping and canceling each other out, resulting in a missing diffraction beam.

3. How does the spacing between the slits affect the diffraction pattern in a diffraction grating?

The spacing between the slits in a diffraction grating determines the angle at which the light is diffracted. A smaller spacing will result in a wider diffraction pattern, while a larger spacing will result in a narrower pattern.

4. What is the difference between a reflection grating and a transmission grating?

A reflection grating is made by coating a surface with a series of parallel lines, while a transmission grating is made by etching slits onto a transparent material. Reflection gratings produce a diffraction pattern by reflecting light, while transmission gratings diffract light as it passes through the slits.

5. How is a diffraction grating used in scientific research?

Diffraction gratings are commonly used in scientific research to study the properties of light, such as its wavelength and intensity. They are also used in spectroscopy to analyze the composition of substances based on the diffraction patterns produced by their atomic or molecular structures.

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