Rayleigh Criterion related to the eye

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SUMMARY

The discussion centers on applying Rayleigh's criterion to determine the effective diameter of the eye's optical system based on its resolving power. The problem states that the resolving power is 1.67×10−2 degrees and the wavelength of light is 550 nm. The formula used is sin(angle) = 1.22 * (wavelength/diameter). The participant consistently arrives at an incorrect answer of 0.0023 mm, indicating a potential misunderstanding of unit conversion or the application of the formula.

PREREQUISITES
  • Understanding of Rayleigh's criterion in optics
  • Familiarity with the concept of resolving power
  • Basic knowledge of unit conversion, particularly between millimeters and nanometers
  • Proficiency in trigonometric functions and their applications in physics
NEXT STEPS
  • Review the derivation and application of Rayleigh's criterion in optical systems
  • Study the relationship between resolving power and optical diameter
  • Practice unit conversion between nanometers and millimeters in optical calculations
  • Explore examples of diffraction-limited systems in physics
USEFUL FOR

Students studying optics, physics educators, and anyone interested in the principles of vision and optical resolution.

wmiddlebrook
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I am doing a Mastering Physics problem that I am stumped on. The question is:

"If this resolving power is diffraction-limited, to what effective diameter of your eye's optical system does this correspond? Use Rayleigh's criterion and assume that the wavelength of the light is 550 nm ."

The resolving power of the eye is 1.67×10−2 degrees.

I know that sin(angle)=1.22*(wavelength/diameter) and I keep getting .0023 mm as the answer and getting it wrong.

WITHOUT giving the answer, how do you approach this problem/ what am I doing wrong?

I am thinking that I need to multiply my number by the diameter of the eye to get the length in the eye, but I am not sure.
 
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Check your units.

ehild
 

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