Question

The Human Eye THE HUMAN EYE: While digital camera form images with pixels, the human eye forms images with rods and cones that lie on the retina. If two point objects close together are to be seen as two distinct objects, the images must fall on the retina on two different cones that are not adjacent. That is, there must be a cone between them. Assume that the cones are sensitive to a wavelength of 550nm. If the iris is about 5mm in diameter, and we can model the human eye as a sphere with roughly a 25mm diameter,

a. What is the minimum separation between two objects at a distance of 2rn away from the eye that we can resolve at this wavelength?

b. What is the distance between the two cones on the retina?

Answer 1

a) If (is in radian) is the angular separation between two distinct objects at a distance 2m away from the eye then

Sin = 1.22×(/D) [ Where = 550 nm =550×10^-9m

= 1.342×10^-4 rad and D = 5mm=5×10^-3 m]

As tends to zero Sin tends to tan

tan= x/2 [where x is the minimum distance between two or, x= 2.tan distinct object situated at a distance 2 m away]

or, x=2.tan(1.342×10^-4)

or, x= 2.648×10^-4 m = 0.2648mm

b) If S is the spacing between two cone cells on the retina then

S= d. [Where d is the diameter of the eye= 25mm

or, S= 25×10^-3×1.342×10^-4 or, d= 25×10^-3m]

or, S= 3.355×10^-6m

= 3.355 micro m.