Resolution and Rayleigh's Criteria

The use of radians in the calculation is preferred in mathematics because it simplifies the formula and gives a more accurate result. The Rayleigh criterion is based on the approximation sin(\theta)≈\theta, which is only valid when using radians.
  • #1
prettykitty
8
0
When working problems using Rayleigh's Criteria:

θmin=1.22 [λ/D]

Why do the answers come out in radians?
I'm sure it has something to do with the aperture being circular but I don't understand why.

Thanks!
 
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  • #2
You can change the units in the formula to degrees if you wish, in which case the constant 1.22 becomes 69.9°. Radians are the preferred unit in mathematics, however. The look direction in an optical system involves the quantity [itex]sin(\theta)[/itex], and [itex]\theta[/itex] is very small when determining resolution. We can use the approximation [tex]sin(\theta)≈\theta[/tex] in deriving the Rayleigh criterion. That approximation is valid as written only for [itex]\theta[/itex] in radians.
 
  • #3
prettykitty said:
When working problems using Rayleigh's Criteria:

θmin=1.22 [λ/D]

Why do the answers come out in radians?
I'm sure it has something to do with the aperture being circular but I don't understand why.

Thanks!

The factor 1.22 is due to a circular aperture- for a square aperture, the numerical factor is 1.
 

What is resolution?

Resolution refers to the ability to distinguish and separate two adjacent points or objects in an image or on a scale. In other words, it is the minimum distance between two points that can be perceived as separate entities.

What is Rayleigh's criteria?

Rayleigh's criteria is a rule that determines the minimum resolution needed to distinguish two closely spaced objects in an image. According to this criteria, the distance between the two objects should be at least equal to the diameter of the Airy disk, which is the central bright spot in the diffraction pattern of a point source of light.

How does wavelength affect resolution?

The wavelength of light plays a crucial role in determining the resolution of an optical instrument. This is because shorter wavelengths, such as those in the blue range, have a higher frequency and can bend more around obstacles, resulting in less diffraction and better resolution compared to longer wavelengths, like those in the red range.

What are the factors that affect resolution?

The resolution of an optical instrument is affected by several factors, including the numerical aperture of the lens, the wavelength of light, and the quality of the lens. Other factors that can impact resolution include the size of the aperture, the distance between the object and the lens, and the presence of aberrations in the lens.

What is the difference between optical and digital resolution?

Optical resolution refers to the physical ability of an optical instrument to distinguish between two closely spaced objects, whereas digital resolution refers to the number of pixels in a digital image. In other words, optical resolution is a measure of the clarity of the image, while digital resolution is a measure of its size and detail.

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