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

Find the separation between two cones of the same type on the fovea of the eye by using the resolving power of the eye Essays Find the separation between two cones of the same type on the fovea of the eye by using the resolving power of the eye Essay Find the separation between two cones of the same type on the fovea of the eye by using the resolving power of the eye Essay 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 eyes 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. (Rayleighs criterion:? = ?/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: ? = 1.22? d Where: ? = resolving power of optical instrument ? = Wavelength of light d = diameter of aperture The resolving power of the eye will not be as high as this calculated theoretical resolving power as although the optical equipment of the eye may be of this power the eyes detection facilities give the brain discreet not continuous signals and so the actual resolving power of the eye will never reach this theoretical value even if the optical facilities of the eye are perfect. As a result we must calculate the separation between two cones using: ? = s Where: s = separation r r = distance Plan: Factors identified affecting the experiment: * The separation of the two light sources. I will vary this to produce a range of distances from which the objects can be resolved. * The perpendicular distance that the viewer of the light sources can be from them and still completely resolve them. This will vary as a direct result of changes to the separation of the light sources. * The size and shape of the light sources. I will control this by shining the light through measured apertures made in black acrylic. I will control the size of the apertures by using a 1mm drill bit to create the holes through which the light sources will be shone, this will also ensure the sources are of a constant shape. * The amount of light that is reflected. I will use a black background surrounding the light sources to ensure that only a minimal amount of light is reflected. * The brightness of the two light sources must be equal to each other, I will achieve this by connecting the light sources in series to the same power source. * The brightness of the light sources must be constant as it is easier to resolve brighter objects. I will control this factor by keeping the voltage of the power source constant. * The wavelength of light must be kept constant by using the same equipment (same L.E.D.s) for each repeat of the experiment. This must be controlled as different colours of light stimulate different cones on the retina and also the wavelength of light affects the calculated value for the resolving power of the eye. * The height of the eye relative to the light sources must be constant and perpendicular. This will be controlled by having the light sources at a height of 1 metre and having the viewer use a metre ruler as a guide to the height of their eyes when resolving the light sources. * The size of the eye and the strength of eyesight must be constant throughout the experiment. This will be achieved by using the same observer throughout the procedure and carrying out the procedure in a single session. * The brightness of the environment must be constant. This will be kept constant by carrying the experiment out in a single session. Also the environment will be kept as dark as possible to maximise the resolving power of the eye and so optimise the accuracy of the results. * 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: ? = s R ? = 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? s = separation of 3 cones r = radius of the eye ? = resolving power in radians Separation between two cones = s 2 Theoretical ? = 1.22? D ? = 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 * Assume all eyes work the same * Assume average green wavelength * Assume only one wavelength from L.E.D. * Assume pupil size is constant * Assume light source is perpendicular * Assume light crosses at the centre of the eye * Assume cones are all of equal size and shape. We can assume this as cones are densely packed in the fovea * Assume refraction at the entrance to the eye is zero. We can assume this as distance r is relatively large compared to the separation of the light sources so we can assume that the light entering the eye is perpendicular to the lens. As a result we can assume similar triangles: Test: I carried out a preliminary experiment using this procedure and found the separation of two cones to be 3.57?10-4m. As this is a factor of 10 away from the literature value for separation I will now alter my procedure by increasing the voltage of the power pack to 6.00v to increase the brightness of the L.E.D.s and so optimise the resolving power of the eye. 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: ? = s = gradient = 3.125?10-4 r Separation of cones = r ? ? 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.