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

In summary, the resolution of the eye is limited by the pupil diameter. To find the smallest diameter spot the eye can produce on the retina, we can use the formula θrad=1.22λ/D, where θ is the resolving angle, λ is the wavelength of light, and D is the diameter of the pupil. Assuming a pupil diameter of 2.59 mm and a light wavelength of 550 nm, we can calculate the resolving angle to be 1.98E-4 radians. Using the hint provided, we can then double the distance from the main axis to the first minimum to find the smallest spot size, which is 10.06 μm. However, the index of refraction of the vit
  • #1
aDabOfRanch
3
0

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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  • #2
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)?
 
  • #3
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
 
  • #4
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?
 
  • #5
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.
 

What is the resolving power of the eye?

The resolving power of the eye refers to its ability to distinguish between two closely spaced objects. It is measured in terms of the minimum angular separation between two points that can still be perceived as distinct by the eye.

How is the resolving power of the eye determined?

The resolving power of the eye is determined by the density and arrangement of photoreceptors in the retina, specifically the cones. The closer the cones are packed and the smaller their size, the higher the resolving power of the eye.

What factors can affect the resolving power of the eye?

The resolving power of the eye can be affected by various factors such as age, as the density of photoreceptors decreases with age, and the presence of eye diseases or conditions like cataracts or astigmatism which can distort the shape of the eye's lens.

What is the limit of the resolving power of the eye?

The limit of the resolving power of the eye is around 0.02 degrees, which is equivalent to being able to distinguish two objects that are 0.6mm apart at a distance of 1 meter. Beyond this limit, the two objects will appear as one blurred image.

Can the resolving power of the eye be improved?

The resolving power of the eye can be improved with the use of corrective lenses, such as glasses or contact lenses, which can help to correct any refractive errors and improve the focus of light onto the retina. However, the maximum resolving power is limited by the natural structure and function of the eye.

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