## Resolving Power of the Eye

The resolving power of an optical instrument is limited by the wavelength of light and the aperture or opening of the instrument - usually the diameter of the primary/objective lens.We can treat the eye as an optical instrument that focuses light with wavelengths 400 - 700 nm or

\[4 \times 10^{-7} \: m - 7 \times 10^{-7} \: m\]

and the pupil as an aperture of size 5 mm.The eye can then resolve objects using the Rayleigh criterion

\[\theta \simeq \frac{1.22 \lambda }{D}\]

. With the numbers given, \[\theta \simeq \frac{1.22 \times 4 \times 10^{-7}}{5 \times 10^{-3}} = 9.76 \times 10^{-5} \: rads\]

.It may be more useful to translate this into seconds of arc.

\[2 \pi \: rads = 360 \: degrees = 360 \times 60 \: arcminutes = 360 \times 60^2 \: arcseconds\]

&Hence to change rads into arcseconds, multiply by

\[\frac{360 \times 60^2}{2 \pi}\]

.\[9.76 \times 10^{-5} \: rads = 9.76 \times 10^{-5} \times\frac{360 \times 60^2}{2 \pi}=128.5 \: arcseconds\]

.Compare this with the apparent size of the moon subtends an angle of about 1872 arcseconds.