Question

8. The resolution of the eye is 1/x where x is the spatial separation of a line pair. This is often expressed as the angular resolution, which typically is about 1 arc minute per line pair, or about 0.017°. Consider that you are viewing a grating of lines 25 cm from the eye. A. If the lines can just be resolved, how large is the distance between line centers? B. What is the spacing between the lines in the image on the retina? C. In the fovea the light-sensitive areas of the cones are about 3.2 x 10m in diameter and about 2.5 x 10 m separates their centers in close hexagonal packing. Does your answer in part B make sense with respect to this spacing of the cones?

Answer 1

a) The object is placed at a distance of 25 cm = 0.25 m

If the angle between the two lines is greater than 0.017^o , the lines will be clearly visible.

The angle is: 0.017^o = 0.017*3.14/180 = 0.00029655555 radians.

Using the formula angle = arc/radius, the separation between two lines(arc) is given by

angle*radius = 0.00029655555*0.25 = 7.414*10^-5 m.

b) The distance from eye lens to retina is 20 mm = 0.02 m

considering the angle on the either side of the eye to be same,

separation in retina = angle * 0.02 = 0.00029655555*0.02 = 5.9311*10^-6 m

c) The separation between the light sensing part of the cones is given as (3.2+2.5) = 5.7*10^-6 m

So, comparing this with the separation of image in retina for clear resolution, we can see that we get a clear resolution, when the image from two lines fall on two different cone cells.