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

[aDabOfRanch]

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

θ_rad=1.22λ/D

tanθ=Y_m/L

The Attempt at a Solution

Found the resolving angle using θ_rad=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=Y_m/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

 

[gneill]

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)?

 

[aDabOfRanch]

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! λ_film=λ_vac/n which turns out to be 412nm or 0.412μm

 

[gneill]

It causes the light to bend in the eye. I forgot to mention that in my post, sorry! λ_film=λ_vac/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 θ_rad?

 

[aDabOfRanch]

So it alters the wavelength. What value of wavelength did you use when you calculated the value for θ_rad?

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