Diffraction Grating ratio

In summary, the problem involves using a diffraction grating with two different wavelengths of light, λA and λB, and finding the ratio between them. The fourth-order principal maximum of light A overlaps exactly with the third-order principal maximum of light B, leading to the equation 4λA = 3λB. This result demonstrates the conditions required for this to occur, and a slight change in wavelength can make the overlap more precise.
  • #1
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Homework Statement



The same diffraction grating is used with two different wavelengths of light, λA and λB. The fourth-order principal maximum of light A exactly overlaps the third-order principal maximum of light B. Find the ratio λA/λB.

Homework Equations



sin theta = m lambda / width of the slits

The Attempt at a Solution



sin theta 1 = sin theta 2 since they overlap.

3/4

I don't understand how can 4th order principal and 3rd order principle can have the same sin theta? Because, unless I am misunderstanding something, I don't think it's possible for different orders to completely overlap on top of each other so that they meet at the same point on the opposite screen of the diffraction grating.
 
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  • #2
The spacing between fringes depends on the wavelength.
This would happen if, say, light A created fringes 3deg apart and light B 4deg apart - the third fringe of B would be at 12deg which is the same as the 4th fringe of A.

In this case - you are correct:
[itex]4\lambda_A = 3\lambda_B \Rightarrow \frac{\lambda_A}{\lambda_B}=\frac{3}{4}[/itex]

This result demonstrates the conditions required for this to happen.

eg. if λA=330nm then λB=440nm

Ideally I should show you:
colour%20affect%20pattern_colour.png

... the green 2nd order matches with the purple 3rd order. If we tweaked the wavelength only slightly it would be as exact as you like.
 
Last edited:

1. What is a diffraction grating ratio?

A diffraction grating ratio refers to the ratio of the spacing between the lines on a diffraction grating to the wavelength of light being diffracted. It is used to determine the angle at which the light is diffracted and the resulting interference pattern.

2. How is the diffraction grating ratio calculated?

The diffraction grating ratio is calculated by dividing the distance between the grating lines (d) by the wavelength of light (λ).

Diffraction grating ratio = d/λ

3. What is the significance of the diffraction grating ratio?

The diffraction grating ratio is important because it determines the angular dispersion of the diffracted light. A larger ratio means a smaller angular dispersion, resulting in a sharper and more distinct interference pattern.

4. How does the diffraction grating ratio affect the diffraction pattern?

The diffraction grating ratio directly affects the spacing and intensity of the diffraction pattern. A higher ratio leads to a narrower and more intense central peak, while a lower ratio results in a broader and less intense pattern.

5. What factors can affect the diffraction grating ratio?

The diffraction grating ratio can be affected by the quality and precision of the grating, as well as the wavelength of light used. Other factors such as temperature, humidity, and alignment of the grating can also impact the ratio and the resulting diffraction pattern.

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