Max distance of resolution from 2 point sources of light

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SUMMARY

The discussion focuses on calculating the maximum distance from which two point sources of light, separated by 4.91 cm, can be resolved using a 12.1 μm diameter pinhole and red light with a wavelength of 690 nm. The key equation used is sinθ = 1.22*(λ/D), which relates the angle of resolution to the wavelength and diameter of the pinhole. The participant attempts to solve for the distance L using the equation y = L*tan θ but encounters uncertainty regarding the value of y. Clarification is sought on the definition of y in this context.

PREREQUISITES
  • Understanding of the Rayleigh criterion for resolution
  • Familiarity with basic trigonometry and small angle approximations
  • Knowledge of light properties, specifically wavelength and diffraction
  • Experience with optical systems, particularly pinhole cameras
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  • Learn about the implications of the small angle approximation in optics
  • Explore the relationship between wavelength, aperture size, and resolution
  • Investigate practical applications of pinhole cameras in experimental physics
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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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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.
 

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