Calculate lens diameter using NA

In summary, the task is to calculate the lens diameter for an aligner with an object to lens distance of 500mm and a numerical aperture (NA) of 0.28. Using the equation NA = r / D, we can determine that the lens radius (r) is 140mm. However, it is unclear how the idea of 90% of the lens being usable affects the calculation. It is suggested that the lens diameter would still be 280mm, but further clarification is needed.
  • #1
Lanc1988
19
0

Homework Statement


A projection aligner has an object to lens distance of 500mm. Calculate lens diameter for the aligner if NA = 0.28. Assume the usable area of lens is 90% of its diameter.

Homework Equations


NA = r / D
Note: NA is the numerical aperture.

The Attempt at a Solution


I know that NA = r / D which means 0.28 = r / 500 and then r = 140mm so the diameter of the lens would be 280mm but I'm unsure how to use the idea of 90% of the lens being usable.
 
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  • #2
It seems that the answer would still be 280mm but I'm not completely sure. Any help would be appreciated. Thanks.
 

FAQ: Calculate lens diameter using NA

1. How do you calculate lens diameter using NA?

The formula for calculating lens diameter using Numerical Aperture (NA) is D = 2 x NA x f, where D is the lens diameter, NA is the numerical aperture, and f is the focal length of the lens. This formula assumes that the lens is circular and that the NA is measured at the lens surface.

2. What is Numerical Aperture (NA) and why is it important in calculating lens diameter?

Numerical Aperture (NA) is a measure of a lens's ability to capture light from a specific angle. It is calculated as NA = n x sin(a), where n is the refractive index of the medium between the object and the lens, and a is the maximum angle of light that can enter the lens. NA is important in calculating lens diameter because it determines the amount of light that can pass through the lens, which in turn affects the resolution and quality of the image.

3. How accurate is the calculation of lens diameter using NA?

The accuracy of the calculation of lens diameter using NA depends on the accuracy of the input values, such as the refractive index and the maximum angle of light. The formula assumes an ideal lens shape and does not take into account other factors such as lens aberrations. Therefore, the calculated diameter may not be exact, but it can provide a good estimation.

4. Can the calculation of lens diameter using NA be used for all types of lenses?

The formula for calculating lens diameter using NA is applicable to most types of lenses, including spherical lenses, aspherical lenses, and cylindrical lenses. However, for non-circular lenses, the calculation may be more complex and may require additional parameters.

5. Are there any other methods for calculating lens diameter besides using NA?

Yes, there are other methods for calculating lens diameter, such as using the lens's focal length and the object distance. However, these methods may not be as accurate as using NA, especially for lenses with complex shapes or for high NA values. Therefore, using NA is generally the preferred method for calculating lens diameter.

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