Condition for resolution of two point sources of light

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SUMMARY

The discussion centers on the Rayleigh Criterion for resolving two point sources of light, articulated by the formula ##\theta=1.22 \frac{\lambda}{D}##, where D represents the diameter of the circular aperture. Participants clarify that D is equivalent to 2 times the radius (r), leading to the conclusion that ##\theta \geq 1.22 \frac{\lambda}{2r}##. The confusion arises from the interpretation of the relationship between diameter and radius, ultimately affirming that ##r \approx b## is a valid consideration in this context.

PREREQUISITES
  • Understanding of the Rayleigh Criterion
  • Familiarity with light wavelength (##\lambda##)
  • Knowledge of circular aperture concepts
  • Basic trigonometry for angular separation (##\theta##)
NEXT STEPS
  • Study the derivation and applications of the Rayleigh Criterion in optics
  • Explore the effects of aperture size on resolution in optical systems
  • Investigate the relationship between wavelength and resolution in imaging technologies
  • Learn about other criteria for resolution in different contexts, such as the Abbe Criterion
USEFUL FOR

Optics students, physicists, and engineers involved in designing optical instruments or studying light behavior will benefit from this discussion.

songoku
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Homework Statement
Please see below
Relevant Equations
##\theta=1.22 \frac{\lambda}{b}##
1712282564500.png


The formula is ##\theta=1.22 \frac{\lambda}{b}## where b is the diameter of circular aperture

I thought it would be ##\theta \geq 0.61 \frac{\lambda}{r}## since diameter = 2 x radius but the answer is (D)

Do we just consider ##r \approx b## since maybe it is small or am I missing something else?

Thanks
 
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songoku said:
Homework Statement: Please see below
Relevant Equations: ##\theta=1.22 \frac{\lambda}{b}##

View attachment 342834

The formula is ##\theta=1.22 \frac{\lambda}{b}## where b is the diameter of circular aperture

I thought it would be ##\theta \geq 0.61 \frac{\lambda}{r}## since diameter = 2 x radius but the answer is (D)

Do we just consider ##r \approx b## since maybe it is small or am I missing something else?

Thanks
I agree with you.

The Rayleigh Criterion says that when two distant lights sources (wavelength, ##\lambda\,##) are viewed through a circular aperture of diameter, ##D##, they may be resolved provided that there angular separation, ##\theta## (in radians) is such that

##\displaystyle \quad \quad \theta \ge 1.22 \dfrac{\lambda}{D} \ .##

Since ##D=2r## , I agree that the correct answer is C) .
 
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Thank you very much SammyS
 

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