Rayleigh criterion: finding the angular separation between 2 distant points

In summary, The conversation is discussing the steps taken to find an angular separation, with the final result being 2.85 millidegrees. There is a discussion about whether or not to multiply the angle by two, with the conclusion being that there is no need to do so. The conversation also mentions a preference for using radians instead of degrees and a correction to the previously used wavelength. The corrected angle is now 1.4 millidegrees.
  • #1
Bolter
262
31
Homework Statement
See below
Relevant Equations
dsin(theta) = 1.22 lambda
Screenshot 2020-03-24 at 09.45.09.png

I have tried this question and have gotten to an answer from the following steps

IMG_4333.jpg


So my angular separation is 2.85 millidegrees. Have I done this right with the formula I have made use of?

Any help would be great, thanks!
 
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  • #2
All looks good until you get to the end and multiply the angle by two. There is no need to multiply by 2. Look at the diagram. Peak 1 is located at the first minimum of peak 2. That is a single multiple of the angle to the minimum. Yes, peak 2 is located at the first minimum of peak 1, but that is the same angle, not an additional angle.

P.S.: I like radians where for small angles sin(theta) ~= theta. Makes it easier to check the math, among other things.
 
  • Like
Likes Bolter
  • #3
Cutter Ketch said:
All looks good until you get to the end and multiply the angle by two. There is no need to multiply by 2. Look at the diagram. Peak 1 is located at the first minimum of peak 2. That is a single multiple of the angle to the minimum. Yes, peak 2 is located at the first minimum of peak 1, but that is the same angle, not an additional angle.

P.S.: I like radians where for small angles sin(theta) ~= theta. Makes it easier to check the math, among other things.

Yes understood now

Plus I've just realized I've been using the wrong wavelength. It should have been 483 nm NOT 491 nm. Making that adjustment I get the angle to be 1.4 millidegrees now
 

1. What is the Rayleigh criterion?

The Rayleigh criterion is a principle used in optics to determine the minimum angular separation between two distant points that can be resolved by a telescope or other optical instrument. It is based on the concept of diffraction and the ability of a lens or aperture to produce distinct images of two closely spaced objects.

2. How is the Rayleigh criterion calculated?

The Rayleigh criterion is calculated by taking the wavelength of light being observed and dividing it by the diameter of the aperture of the instrument. The result is then multiplied by a factor of 1.22 to account for the effects of diffraction. The resulting value is the minimum angular separation between two points that can be resolved by the instrument.

3. What is the significance of the Rayleigh criterion?

The Rayleigh criterion is important because it sets a limit on the resolution of optical instruments. It helps determine the quality and capabilities of telescopes, microscopes, and other optical devices. By understanding the Rayleigh criterion, scientists can design and improve instruments to better observe and study distant objects.

4. Can the Rayleigh criterion be applied to all types of light?

Yes, the Rayleigh criterion can be applied to all types of light, including visible light, infrared, and ultraviolet. However, the value of the criterion will vary depending on the wavelength of the light being observed. For example, shorter wavelengths of light will have a smaller minimum angular separation compared to longer wavelengths.

5. Are there any limitations to the Rayleigh criterion?

Yes, there are some limitations to the Rayleigh criterion. It assumes that the two points being observed have the same intensity and are of equal size. In reality, this may not always be the case, and the criterion may not accurately predict the resolution of the instrument. Additionally, other factors such as atmospheric conditions and imperfections in the instrument can also affect the resolution.

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