Max distance of resolution from 2 point sources of light

AI Thread Summary
The discussion focuses on resolving two point sources of light separated by 4.91 cm 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 helps calculate the angle θ for resolution. Participants suggest using the relationship y = L*tan θ to find the maximum distance L from which the sources can be resolved. The challenge arises in determining the value of y, with clarification that y represents the distance between the sources as viewed from the pinhole. The small angle approximations are recommended for simplifying calculations.
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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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