Diffraction Grating, Maxima, finding slit seperation

In summary, incident light with a wavelength of 680 nm is diffracted by a grating, resulting in adjacent maxima at angles given by sin θ = 0.2 and sin θ = 0.3. The fourth-order maxima are missing. The smallest slit width this grating can have can be found using equations that relate slit width to angle theta, with the condition that m2=m1+1. The information that the maxima are adjacent is enough to determine both d (slit width) and m1, m2 (diffraction orders). In the second part of the problem, the same equation can be used to find the minimum size of the slit, with the condition that there are only
  • #1
Oijl
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Homework Statement


Light of wavelength 680 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by sin θ = 0.2 and sin θ = 0.3, respectively. The fourth-order maxima are missing.

(b) What is the smallest slit width this grating can have?

Homework Equations

The Attempt at a Solution


What equations relate slit width to angle theta?
 
Last edited:
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  • #2
The diffraction orders do not have to be 1 and 2. Actually they are not.
You don't need to assume their values. The information that the maxima are adjacent is enough. With your notation, that means m2=m1+1.
You can find both d and m1,m2 from the equations (with the above condition).
 
  • #3
Yes, I had tried that, but it gave me values that I thought were too far from the correct answer (which I knew the value of). I've looked at all the numbers more closely, and it's just rounding preferences, is all the matter.

Thanks.
 
  • #4
I edited the first post, to make it about the second part of the problem, for which I cannot think of any equations.
 
  • #5
There is nothing about rounding. The diffraction orders are 1 and 2 (in the first part).
The same equation will give the minimum size of the slit. The condition is that you have only the maxima with orders 0 to 3 and nothing at 4.
That means that the sin(theta) will have to be l>= 1 for order 4.
 
  • #6
There is nothing about rounding. The diffraction orders are 2 and 3 (in the first part).
The same equation will give the minimum size of the slit. The condition is that you have only the maxima with orders 0 to 3 and nothing at 4.
That means that the sin(theta) will have to be l>= 1 for order 4.
 

1. What is a diffraction grating?

A diffraction grating is a device used to split and diffract light into its component wavelengths. It consists of a large number of parallel, evenly spaced slits that act as individual sources of light waves.

2. What are maxima in diffraction gratings?

Maxima in diffraction gratings refer to the bright spots of light that are produced when the light waves passing through the slits interfere constructively. These maxima correspond to the wavelengths of light that are diffracted at a specific angle.

3. How do you find the slit separation in a diffraction grating?

The slit separation in a diffraction grating can be found by using the equation dsinθ = mλ, where d is the slit separation, θ is the angle of diffraction, m is the order of the maxima, and λ is the wavelength of light. Rearranging the equation, d = mλ/sinθ. This can be used to calculate the slit separation for different orders of maxima.

4. What factors affect the diffraction pattern in a diffraction grating?

The main factors that affect the diffraction pattern in a diffraction grating are the slit separation, the wavelength of light, and the angle of incidence. The number of slits and the type of light source used can also have an impact on the diffraction pattern.

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

Diffraction gratings are commonly used in scientific research for analyzing the composition of light and determining the wavelengths of different light sources. They are also used in spectroscopy to study the spectral lines of various elements and molecules. Additionally, diffraction gratings are used in optical instruments such as telescopes and cameras to enhance the resolution and clarity of images.

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