Chapter 24, Problem 80RPP

BIO What is 20/20 vision? Vision is often measured using the Snellen eye chart, devised by Dutch ophthalmologist Herman Snellen in 1862 (see Figure 24.29). With normal vision (20/20 vision), you can distinguish a letter that is 8.8 mm high from other letters of similar height at a distance of 6.1 m (20 ft) (the Snellen chart in the figure is smaller than normal size). If your vision is 20/40, the letters must be twice as high to be distinguishable. Alternatively, a person with 20/40 vision could distinguish letters from 20 ft that a person with 20/20 vision can distinguish at 40 ft. Someone with 20/60 vision could distinguish letters at 20 ft that someone with 20/20 vision could distinguish at 60 ft.

Does the Rayleigh criterion limit visual resolution? Assume that the eye's pupil is 5.0 mm in diameter for 500-nm light. The Rayleigh criterion angular deflection for such light entering the eye's pupil is

$\alpha =1.22\frac{500\times {10}^{-9}\text{m}}{5.0\times {10}^{-3}\text{m}}=1.2\times {10}^{-4}\text{ rad}$

If the Rayleigh criterion limited visual resolution, then from a distance of 6.1 m, you should be able to distinguish details in shapes of size

$y=L\tan \alpha =(6.1m)[tan(1.2\times {10}^{-4}\text{rad)]=0}\text{.7}\times {\text{10}}^{-3}\text{m=0}\text{.7 mm}$ or about one-tenth the size of the 8.8-mm-tall letter in row 8 (20/20 vision) of the full-size Snellen eye chart. Thus, according to the Rayleigh criterion, we should easily be able 10 resolve different 8.8-mm-tall letters. Other factors, such as chromatic aberration, irregularities in the comea-lens-retina shapes, the density of rods and cones in the retina and air currents, limit visual resolution more than the Rayleigh criterion diffraction limit.

If the vision of a hawk is 20/5. then what is the angular resolution of the hawk?

$\begin{array}{l}\begin{array}{l}\text{a}\text{. 0}\text{.2 }\times {\text{ 10}}^{\text{-4}}\text{rad}\hfill \\ \text{b}\text{. 0}\text{.5 }\times {\text{ 10}}^{\text{-4}}\text{rad}\hfill \\ \text{c}\text{.1}\times {\text{10}}^{\text{-4}}\text{rad}\hfill \end{array}\\ \text{d}\text{. 4 }\times {\text{ 10}}^{\text{-4}}\text{rad}\end{array}$