What is the spatial resolution of the eye for two red lights separated by 5cm?

In summary, the angular resolution of the eye is about 1 min of arc = 1/60th of a degree and the spatial resolution is 5cm.
  • #1
captainjack2000
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0

Homework Statement


Two red lights are separated by 5cm, perpendicular to your line of sight. How far away from them are you if they can just be resolved with the naked eye?

Homework Equations


angular resolution =sin(theta)=1.22lambda / D
spatial resolution = 1.22(focal length * lambda)/D

The Attempt at a Solution


the angular resolution of the eye is about 1 min of arc = 1/60th of a degree
the wavelength of red light is about 650nm
In the equation above D is diameter of the eye's pupil - approximately 5mm?
spatial resolution=5cm

I am not quite sure how to put all this information together?
using the information I have;
5cm=1.22(focal length *650nm)/5mm
which gives the focal length of 315 m
 
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  • #2
You seem to have mixed up multiple ways of solving this.

If you are given 1' as the resolution then it's simply a triangle - 1' vertex and a base 5cm wide = find how long it it. (hint an angle this small sin(angle) = angle ,in raidans)

If you are assuming this is the diffraction limit of the eye then you need the diameter of the pupil and the wavelength to get the angle. Then the same as above.

Either way the focal length doesn't come into it
 
  • #3
We are only given the separation distance of the red lights but I think it is assumed that we know the wavelength of the light and the angular resolution of the eye.

Since the angle is so small and sin(theta)=theta can it also be assumed that tan(theta)=theta? If so the vector triangle would give theta=5cm/distance where theta is 1/60th of a degree=2.9E-4 degrees
distance =171.89m

Am I still doing this wrongly?
When do you use the equation resolution=1.22lambda/D?

thanks
 
  • #4
Yes, 1 arc-min is 290 micro-rad, so the distance is 0.05m / 290e-6 = 170m
With angles this small tan=sin=theta

Or if you want to use the diffraction limit, (remember 1.22 is for the half angle)
= 2.44 wavelength / d = 2.44 * 600e-9 / 0.005 = 0.00029 rad = 290 microrad = same answer
 
  • #5
thank you that makes much more sense now
:smile:
 

1. What is the angular resolution of the human eye?

The angular resolution of the human eye is the smallest angle at which two points can be distinguished as separate entities. It is typically measured in minutes of arc (1/60th of a degree) and varies between individuals, but is generally accepted to be around 1 arcminute or 0.02 degrees.

2. How does the angular resolution of the eye compare to that of a camera?

The angular resolution of the eye is generally considered to be much higher than that of a camera. This is because the eye has a complex structure and constantly adjusts its focus and aperture to optimize vision, whereas a camera has a fixed lens and aperture. However, some high-end cameras are designed to have similar or even better angular resolution than the human eye.

3. Can the angular resolution of the eye be improved?

The angular resolution of the eye is primarily determined by the size and structure of the retina. While it is possible to improve the angular resolution through corrective lenses or surgery, it is limited by the physical capabilities of the eye. However, it is also influenced by factors such as lighting and contrast, which can be optimized to improve visual acuity.

4. Does age affect the angular resolution of the eye?

Yes, the angular resolution of the eye tends to decrease with age. This is due to changes in the structure of the eye, particularly the lens, which becomes less flexible and may develop cataracts. These changes can cause a decrease in visual acuity and a decrease in the angular resolution of the eye.

5. How does the angular resolution of the eye impact vision?

The angular resolution of the eye is an important factor in determining the sharpness and clarity of vision. A higher angular resolution allows for better discrimination between objects and details, which is crucial for tasks such as reading, driving, and recognizing faces. A lower angular resolution can lead to blurry or distorted vision and may require corrective measures to improve visual acuity.

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