What Is the Smallest Spot Diameter the Human Eye Can Detect?

AI Thread Summary
The smallest spot diameter the human eye can detect is influenced by the pupil diameter and the wavelength of light. With a pupil diameter of 2.59 mm and a wavelength of 550 nm, the resolving angle was calculated to be approximately 1.98E-4 radians. The distance to the first minima was found to be 5.03 μm, leading to a calculated spot size of 10.06 μm, although the correct answer is 9.85 μm. The index of refraction of the vitreous humor alters the wavelength of light, which affects the calculations. Using the correct wavelength of 0.412 μm instead of 0.42 μm was crucial for accurate results.
aDabOfRanch
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Homework Statement


The resolution of the eye is ultimately limited by the pupil diameter. What is the smallest diameter spot the eye can produce on the retina if the pupil diameter is 2.59 mm? Assume light with a wavelength of λ = 550 nm. (Note: The distance from the pupil to the retina is 25.4 mm. In addition, the space between the pupil and the retina is filled with a fluid whose index of refraction is n = 1.336.)
Hint: The size of the spot is twice the distance from the main axis to the first minimum.

Homework Equations


θrad=1.22λ/D

tanθ=Ym/L

The Attempt at a Solution


Found the resolving angle using θrad=1.22λ/D where D is the diameter of the pupil, and the angle turned out to be 1.98E-4 radians. Then I used the angle to find the distance from the main axis to the first minima by plugging in θ into tanθ=Ym/L solving for Y1 I got 5.03
Using the hint provided I doubled 5.03 to get 10.06μm however the answer is 9.85μm
 
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Hi aDabOfRanch,

Welcome to Physics Forums!

What do you think might be the effect of the index of refraction of the vitreous humor (fluid filling the eye)?
 
gneill said:
Hi aDabOfRanch,

Welcome to Physics Forums!

What do you think might be the effect of the index of refraction of the vitreous humor (fluid filling the eye)?
It causes the light to bend in the eye. I forgot to mention that in my post, sorry! λfilm=λvac/n which turns out to be 412nm or 0.412μm
 
aDabOfRanch said:
It causes the light to bend in the eye. I forgot to mention that in my post, sorry! λfilm=λvac/n which turns out to be 412nm or 0.412μm
So it alters the wavelength. What value of wavelength did you use when you calculated the value for θrad?
 
gneill said:
So it alters the wavelength. What value of wavelength did you use when you calculated the value for θrad?

I used λfilm but I wrote 0.42μm instead of 0.412μm which was messing up the calculations.Thank you.
 

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