Rayleigh Criterion and Resolving Power
By Rayleigh's criterion, two point sources are just resolved when the principal maximum of one diffraction pattern coincides with the first minimum of the other. For a circular aperture of diameter D, the limiting angle is approximately 1.22 lambda/D.
Why this shows up in the exam
Telescope objective sizing · Microscope resolution · Camera aperture trade-offs
Learn the idea
Diffraction limits how closely two distant point sources can be distinguished. A telescope turns each star into a small diffraction spot. Two stars blur together unless their spot patterns are separated enough.
🧠 Memory hook: Bigger aperture, smaller diffraction blur.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- theta_min = 1.22 lambda/D — Rayleigh limit for a circular aperture
- resolving power = 1/theta_min — angular resolving power
How to approach it
- 1Identify aperture shape and dimension
- 2Use consistent angular units
- 3Solve the Rayleigh relation for the requested quantity
Common slip-ups that cost marks
- •Using radius when the formula requires diameter
- •Dropping the factor 1.22 for a circular aperture
- •Confusing magnification with resolution
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A real object is placed 30 cm from a converging lens of focal length 10 cm. Find the real image distance.
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