QuestionJune 4, 2025

Describe how the Rayleigh criterion applies to the human eye

Describe how the Rayleigh criterion applies to the human eye
Describe how the Rayleigh criterion applies to the human eye

Solution
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Answer

The Rayleigh criterion for the human eye gives a minimum angular resolution of approximately 1.22 \times 10^{-4} radians. Explanation 1. Define Rayleigh Criterion The Rayleigh criterion states that two point sources are resolvable when the central maximum of one diffraction pattern coincides with the first minimum of the other. 2. Apply to Human Eye For the human eye, the Rayleigh criterion determines the smallest angular separation at which two points can be distinguished. This depends on the wavelength of light and the diameter of the pupil. 3. Calculate Minimum Angular Resolution **Formula:** \theta = 1.22 \frac{\lambda}{D}, where \theta is the angular resolution, \lambda is the wavelength of light, and D is the diameter of the pupil. 4. Typical Values for Human Eye Assuming \lambda = 550 \text{ nm} (average visible light) and D = 5 \text{ mm} (average pupil size), calculate \theta.

Explanation

1. Define Rayleigh Criterion<br /> The Rayleigh criterion states that two point sources are resolvable when the central maximum of one diffraction pattern coincides with the first minimum of the other.<br /><br />2. Apply to Human Eye<br /> For the human eye, the Rayleigh criterion determines the smallest angular separation at which two points can be distinguished. This depends on the wavelength of light and the diameter of the pupil.<br /><br />3. Calculate Minimum Angular Resolution<br /> **Formula:** $\theta = 1.22 \frac{\lambda}{D}$, where $\theta$ is the angular resolution, $\lambda$ is the wavelength of light, and $D$ is the diameter of the pupil.<br /><br />4. Typical Values for Human Eye<br /> Assuming $\lambda = 550 \text{ nm}$ (average visible light) and $D = 5 \text{ mm}$ (average pupil size), calculate $\theta$.
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