1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Human Eye problem

  1. Sep 18, 2013 #1
    1. The problem statement, all variables and given/known data

    A) Under optimum conditions, the smallest black dot that can be seen subtends an angle of 2.3 x 10-6 rad. If a dot is viewed at a distant of 0.25 m, the near point of a normal adult, what is the smallest diameter it can have and still be seen? B) The maximum resolution is obtained when the image falls on the fovea centralis. At 10° away from this region, the acuity is 10 times poorer. What is the minimum size spot that can be seen at that angle under these conditions?

    2. Relevant equations

    Pf = 1/xf + 1/D

    Pf = person's far point, 1/xf = distance a person sees an object, D = image distance

    Pn = 1/xn + 1/D

    Pn person's near point, 1/xn - distance a person sees an object, D = image distance

    A = Pn - Pf

    A = power of accommodation

    sin θ = 1.22 (λ/d)-power of acuity equation

    λ = wavelength, d = diameter


    3. The attempt at a solution

    I've puzzled over this problem. I'm not sure what the relevant equation would be unless I'm missing one. Any help is appreciated.
     
  2. jcsd
  3. Sep 18, 2013 #2
    You are given a distance to the dot. The dot is essentially a small circle perpendicular to that distance. Its diameter and the distance to the eye form a right triangle. Your are also given an angle in this triangle.
     
  4. Sep 18, 2013 #3
    I guess I feel like I'm missing something. I'm not given a wavelength of which this object is being viewed. I otherwise say I could algebraically solve for d that way from the acuity equation. Otherwise I'm not really sure what else to consider...
     
  5. Sep 18, 2013 #4
    Have you drawn a diagram as per #2?
     
  6. Sep 18, 2013 #5
    Attached is the diagram I drew out for it. Am I thinking about it right? I honestly have no idea how to set it up as we did not cover this topic much in class...
     

    Attached Files:

  7. Sep 18, 2013 #6
    See my go at it.
     

    Attached Files:

  8. Sep 18, 2013 #7
    Oh! Ok so I took .25 m * sin (2.3 * 10^-7 ) and got d = 5.75 * 10^-7 m. Thank you!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Human Eye problem
  1. Human eye optics (Replies: 5)

Loading...