Max distance of resolution from 2 point sources of light

In summary, the problem involves determining the maximum distance at which two point sources of light can be resolved when viewed through a 12.1 μm diameter pinhole and using red light (λ = 690 nm). This can be solved using the equations sinθ = 1.22*(λ/D) and y= L*tan θ, where θ is the angle between the two sources as viewed from the pinhole and y is the distance between the pinhole and the sources. The small angle approximations θ ≈ sinθ ≈ tanθ may be used in this problem.
  • #1
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Homework Statement


Two point sources of light are separated by 4.91 cm. As viewed through a 12.1 μm diameter pinhole, what is the maximum distance from which they can be resolved if red light (λ = 690 nm) is used?


Homework Equations


sinθ = 1.22*(λ/D)

y= L*tan θ



The Attempt at a Solution


Using sinθ = 1.22*(λ/D) , I solve for θ. Then using θ I put it into the second equation,
y= L*tan θ.

I should then be able to solve for L, but the problem is i don't know what y is, or what value i can use for y. Any suggestions? Thanks in advance
 
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  • #2
Have you drawn a diagram? Looks like L is the distance between the pinhole and the two sources, and θ is the angle between the two sources as viewed from the pinhole. What would that make y?

p.s., the small angle approximations θ ≈ sinθ ≈ tanθ may be used here.
 
  • #3
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Hello, thank you for your question. I can provide you with a solution to this problem.

First, let's define the variables in the problem. θ is the angle between the two point sources of light, λ is the wavelength of the light, D is the distance between the two point sources, and L is the distance from the pinhole to the point where the two sources are being viewed.

To solve for L, we can use the formula y = L*tanθ. However, as you mentioned, we do not know the value of y. In this case, we can use the diameter of the pinhole, which is given as 12.1 μm. We can assume that y is equal to half of the diameter, which is 6.05 μm.

Now, let's solve for θ using the formula sinθ = 1.22*(λ/D). Plugging in the values, we get: sinθ = 1.22*(690 nm / 4.91 cm) = 0.0001725.

To find the maximum distance, we need to solve for L using the formula y = L*tanθ. Plugging in the values of y and θ, we get: L = y / tanθ = (6.05 μm) / (0.0001725) = 35,072 μm.

Therefore, the maximum distance from which the two point sources of light can be resolved is 35,072 μm, or 35.072 mm.

I hope this helps. Let me know if you have any further questions. Thank you.
 

1. What is meant by "Max distance of resolution"?

The "Max distance of resolution" refers to the maximum distance at which two point sources of light can be distinguished as separate entities. It is also known as the Rayleigh criterion, and is used to determine the limit of resolution for optical systems.

2. How is the max distance of resolution calculated?

The max distance of resolution is calculated using the Rayleigh criterion, which states that two point sources can be distinguished as separate if the center of one source falls on the first dark ring of the diffraction pattern of the other source. This distance is given by the equation: d = 1.22λ/θ, where d is the distance, λ is the wavelength of light, and θ is the angular separation between the two sources.

3. What factors affect the max distance of resolution?

The max distance of resolution is affected by several factors, including the wavelength of light, the size of the point sources, and the quality of the optical system. In general, shorter wavelengths and smaller point sources will result in a larger max distance of resolution, while a higher quality optical system can improve the resolution.

4. Why is the max distance of resolution important in scientific research?

The max distance of resolution is important in scientific research because it determines the smallest details that can be resolved in an image. This is crucial for studying microscopic objects, such as cells and molecules, and for obtaining accurate measurements in various fields of science, such as astronomy and biology.

5. Can the max distance of resolution be improved?

Yes, the max distance of resolution can be improved by using shorter wavelengths of light, increasing the quality of the optical system, and using advanced techniques such as super-resolution microscopy. However, there will always be a limit to the resolution that can be achieved due to the wave nature of light and the Rayleigh criterion.

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