Diffraction Limited Object Size

  • Thread starter dancergirlie
  • Start date
  • Tags
    Diffraction
In summary, the diffraction-limited object size imposed by the numerical aperture of the eye is approximately 2 times the wavelength divided by the diameter of the iris. Using the given values of 4mm for the iris diameter and 550nm for the wavelength, the diffraction limit is about 1.6775E-4 radians. To find the object size, you can use the paraxial approximation for small angles and multiply the half angle by the distance of 25 cm.
  • #1
dancergirlie
200
0

Homework Statement



What is the diffraction-limited object size (at 25 cm) imposed by the numerical aperture of the eye (if the eye is a diffraction-limited optic)? Use 4mm for the iris diameter and 550 nm for the wavelength.

Homework Equations


Rayleigh criterion states: for angular resolution, theta:
sin(theta)=1.22(wavelength)/Diameter


The Attempt at a Solution



I can solve for the angular resolution, which I got as 1.6775E-4. However, I don't know how to solve for the object size from that. Any help would be great!
 
Physics news on Phys.org
  • #2
if you have an angle and a distance - you can get the size.
Picture it as a narrow triangle of rays going from your eye to a distance of 25cm.
- draw a diagram.

Hint. if the angle is small and in radians then it's even easier
 
  • #3
would I have to take the half-angle of that in order to make a right triangle, or is the angle that I solved for before? If I do have to take the half angle, would I have to multiply the object size by 2?
 
  • #4
Yes the formula you have is for the half angle.
The diffraction limit (in radians) is approx 2 * wavelength / diameter

You should also learn somethign about the sin() of small angles in radians,
 
  • #5
wouldn't that have to be tangent and not sin. Yes, I know about paraxial approximation where tantheta and sintheta would be approximately theta. So, I would take 2*25E-2m*(theta)?
 

What is diffraction limited object size?

Diffraction limited object size refers to the smallest size at which an object can be resolved by an optical instrument. It is determined by the amount of diffraction that occurs as light passes through the aperture of the instrument.

Why is diffraction limited object size important?

Understanding the diffraction limited object size is important for optical scientists and engineers, as it helps determine the capabilities and limitations of optical instruments. It also affects the quality and resolution of images produced by these instruments.

How is diffraction limited object size calculated?

The diffraction limited object size is calculated using the Rayleigh criterion, which states that two point sources of light can be resolved as separate objects if the center of one's diffraction pattern coincides with the first minimum of the other's diffraction pattern. The diameter of the aperture of the instrument and the wavelength of light being used are also factors in the calculation.

Can diffraction limited object size be improved?

While diffraction limited object size cannot be completely eliminated, it can be improved by using larger apertures and shorter wavelengths of light. This is why telescopes and microscopes with larger apertures and shorter wavelengths are able to produce clearer and more detailed images.

How does diffraction limited object size affect the resolution of an image?

The diffraction limited object size affects the resolution of an image by limiting the smallest details that can be distinguished. When the diffraction limited object size is smaller than the details in an image, these details will not be resolved and the image will appear blurry or lacking in detail.

Similar threads

  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
2K
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
808
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
2
Views
9K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
971
Back
Top