Animals
Vision and Diffraction
Take-Home Experiment Write-Up
Background
The pupil in your eye is a circular aperture causing light that passes through it to diffract. When
light from a point source enters your eye, the image on your retina is a certain size and makes
an angle from center to edge with respect to your pupil of
1  1.22
eye
D
where λeye=λair/1.33. We are ignoring the secondary rings because they are much dimmer.
θ
θ1
1
1
θ
Figure 1: Light from two point sources enters your eye making an angle θ with respect to your
pupil. Two central maxima fall on the retina at the back of the eye also subtending an angle θ at
your pupil. θ1 is the angle subtended by the radius of the central maximum. According to
Rayleigh's criterion, the point sources are resolvable if θ ≥ θ1.
If you look at two point sources Rayleigh’s criterion states that you will be able to resolve them
(tell that there are two point sources instead of just one) if the angle, θ, they make with respect
to your eye is greater than or equal to θ1.
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Results
Rayleigh’s criterion gives the angle of minimum resolution for a given wavelength and pupil size.
Figure 2 shows that the angle two objects make with respect to your eye relates to the
separation between the two objects and the distance you are away from the two objects by
  s
L tan   
2 2
Here we are considering large distances L and small separation s so that we can assume is
small and use tan     for small angles. This gives
L  s
For a given separation s and for θ = θ1 we can find the predicted distance L at which you would
resolve the two lines according to Rayleigh’s criterion.
s
paper
θ
L
pupil
D
Figure 2. Two green dots spaced by s on a paper a distance L away from the pupil of your eye
subtend an angle θ with respect to your eye.
For two red lines (λair = 650 nm) about 0.5 cm thick placed so that the inner edges were 1 cm
apart. Three distances measured where the lines were thought to be separable were taken as
37 m, 34 m, and 42 m. The average is 38 m. The experimenter’s pupil size was measured to
be 3 mm, which gives a predicted distance of 50 m. Possible sources of error are difficulty in
measuring a long distance straightly (maybe a string could help with this), difficulty in
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judgement, error in measuring the pupil size (you may find that when the ruler is placed near
your eye your pupils size goes up), and imperfections in the eye (even if you wear glasses you
can not expect the glasses perfectly correct aberrations in the lens and cornea), lastly we are
guessing the wavelength of the light.
Answers to questions to think about:
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How do we use Rayleigh’s criterion to find the predicted maximum distance set by
diffraction at which you could still resolve the lines?
Answer described above in results.
How will what colour marker you use affect your result?
θ1 is proportional to λair and the predicted distance at which you can barely resolve the
lines is inversely proportional to θ so that for larger wavelengths you expect the
predicted distance to decrease.
Why is it mentioned that if you need glasses you should wear them? What assumption
about your eyesight is Rayleigh’s criterion making?
Rayleigh’s criterion is only based on diffraction through a circular aperture it does not
take into account imperfections in eyesight.
You should make the lines thick enough so that you can see them clearly, should you
measure how close the two felt lines are by measuring the distance between the inner
edges, outer edges or centers of the lines?
If you drew two fat lines and put them very close it is still only the distance between the
two lines that you have to take into account.
What are the point sources in this experiment?
Every point on the lines is technically a point source so we are considering the point
sources along the edges of the lines.
How do you think the results differ depending on different lighting intensities of your
surroundings? (i.e. outside on a sunny day for example versus in a darker area inside)
For darker conditions your pupil size goes up and the predicted θ1 goes down. Whether
or not that will help you see at further distances is unclear as you also have more
difficulty seeing in darker conditions (i.e. you can’t see at all in the dark no matter how
big your pupils are!). An eager student could do this experiment say outdoors on a
sunny day versus indoors to see if there is a difference that would relate to the difference
in pupil size.
An interesting aside: an older person in the same lighting conditions whose pupil sizes
are smaller would not be predicted to resolve the lines at as far a distance as a younger
person.
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