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# Find the separation between two cones of the same type on the fovea of the eye by using the resolving power of the eye.

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Introduction

Resolving Power Of the Eye

Objective: Find the separation between two cones of the same type on the fovea of the eye by using the resolving power of the eye.

Introduction: The retina contains two types of light detecting cells: rods and cones. Cones provide the eye’s colour sensitivity, rods, though more sensitive than cones do not detect colour. There is an area on the retina with a much higher density of cones called the fovea. When an object is observed its image is focused on the fovea. The fovea is a 0.3mm diameter area containing on rods and very thin densely packed cones. Cones can be divided into three types; one type detects each of red, green and blue light. The green and red cones are concentrated in the fovea centralis.

To measure the separation between two cones in the eye we can use the resolving power of the eye, for two objects to be resolved optically the viewer must be able to clearly differentiate two distinct bodies. (Rayleigh’s criterion:θ = λ/d)

Critical case shown where objects are just resolved

For two light sources of the same wavelength to be resolved the light must stimulate two cones on either side of one unstimulated cone.

Resolving power due to a circular aperture can be calculated by:

θ = 1.22λ

d

Where:            θ = resolving power of optical instrument

λ = Wavelength of light

Middle

The diameter of the pupil must be kept constant and as large as possible to allow as much light into the eye as possible. This will be kept constant as a direct result of controlling the brightness of the environment. (Variation of 1mm to 10mm possible.)

Method: Set up the apparatus as shown in the previous diagram, switch on the power pack at 3.00v. Turn off the lights in the room and block out daylight coming from any windows or doors. Allow 2 minutes for the eyes to adjust to this darkness and do not allow any light into the room from this point up until the end of the procedure. The viewer of the lights must then stand on the masking tape and back away from the light sources following the masking tape using a metre ruler as a guide to the height of their eyes. The viewer must back away until they are at the point where they can just resolve the two light sources. This point must then be marked on the masking tape using the metre ruler as a guide. Repeat the experiment for this separation three times to obtain a reliable result and eliminate any anomalous results. Three is enough results to obtain a good average result as long as all the results are relatively close together.

Remove the acrylic and replace with another piece of acrylic with holes of different separations and repeat the above procedure. 5 different separations must be used as six results are sufficient to plot a straight-line graph and the sixth result can be 0,0. Less results than this may not produce an accurate gradient and more results would be surplus to requirements. When the experiment is completed measure the marks recorded on the tape for distances and then calculate an average distance for each separation. Plot a line graph of separation against average distance. The graph is plotted to produce a gradient to obtain a value for the resolving power of the eye the graph will reduce any overall errors in the experiment.

Separation of apertures is to be measured with a travelling microscope accurate to ±0.005mm, this measuring equipment is to be used as it is the most accurate available to me in the lab and so will reduce the errors in my results by as much as possible. The other measurement to be taken is the distance from the objects from whence they can be resolved. This is to be measured using a measuring tape accurate to ±0.5cm this is sufficiently accurate as it is a very small error compared to the overall distance and so will not detract significantly from the accuracy of my results.

When the results have been taken the calculation shown overleaf will be used to calculate the separation of two cones on the fovea.

Safety: Electrical equipment must be used with care and it must be ensured that no water is brought into contact with it.

Care must be taken whilst carrying out a procedure in a darkened room, ensure all sharp corners and protruding objects are cleared.

Calculation:

Equation 1: θ = s

R

θ = resolving power of the eye in radians

s = separation of apertures

r = Distance away from light sources when resolving is just possible

Equation 2: s’ = r’θ

s’ = separation of 3 cones

r’ = radius of the eye

θ = resolving power in radians

Separation between two cones = s’

2

Theoretical θ = 1.22λ

D

λ = wavelength of light

D = Diameter of pupil

Assumptions:

• Assume pupil size is constant
• Assume diameter of the eye is 26mm
• Assume no aberrations of the eye
• Assume room is pitch black
• Assume L.E.D.s are of constant brightness
• Assume apertures are spherical

Conclusion

I will test the accuracy of my results by carrying out the experiment in a bright room, resolving two black objects of a similar size to the apertures used in my procedure. Resolving power in this situation should be less than resolving power calculated in the results.

Conclusion:

θ = s  = gradient = 3.125×10-4

r

Separation of cones = r ×θ

r = 1.3×10-2

= 4.062×10-6m = separation between 3 cones

÷2

= 2.03×10-6m = separation between 2 cones

Errors:

This value is appropriate but it must be taken into account that the following errors will affect the final value:

## Equipment

Tape measure accurate to ± 0.01m                                0.05× 100 = 3.13%

Use of tape measure accurate to ± 0.05m                         1.60

Travelling  microscope accurate to ± 0.01×10-3m                0.01×10-3m × 100 = 2.27%

Use of travelling microscope: error as above.                0.44×10-3m

## Other errors

Assumption that the eye is 1.3 ×10-2 radius is a statistical average value and so may vary considerably.

Refracted angle is negligible is an assumption which will affect the accuracy of the results as using this assumption we can use similar triangles to calculate the separation of two cones.

Given these errors be taken into account my value is close enough to the literature value for the separation of two cones to confirm that my procedure was valid.

Appendix:

1. World book 2001. Chicago: World Book Inc, 2001: page 460.
1. http://hyperphysics.phy-astr.gsu.edu/hbase/vision/rodcone.html
1. Advanced physics for you: Keith Johnson, Simmone Hewett, Sue Holt, John Miller, Nelson Thornes ltd. 2000

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