Chapter 24, Problem 77RPP

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

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

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

$\begin{array}{l}y=L\text{ tan }a\text{ =}\left(6.1\text{m}\right)\left[\text{tan}\left(1.2\times {10}^{-4}\text{ rad}\right)\right]\\ =0.7\times {10}^{-3}\text{m = 0}\text{.7mm}\end{array}$ 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 comes-lens-retime shapes, the density of rods and cones In the retina and air currents, limit visual resolution more than the Rayleigh criterion diffraction limit.

Suppose that a person with 20/20 vision stands 30 ft from a Snellen eye chart. Which answer below is closest to the minimum height of the letters the person can distinguish?

a. 4.4 mm

b. 6.6 mm

c. 8.8 mm

d. 1.3 mm

e. 1.8 mm