Resolving Power of the Eye

The resolving power of an optical instrument is limited by the wavelength of light and the aperture of the instrument - usually the diameter of the objective or primary lens.
We may 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 an aperture - the size of the pupil as - of up to 5 mm.
The eye can then resolve objects according to the Rayleigh criterion  
\[\theta \simeq \frac{1.22 \lambda }{D}\]
. With the numbers as above,  
\[\theta \simeq \frac{1.22 \times 4 \times 10^{-7}}{5 \times 10^{-3}} = 9.76 \times 10^{-5} \: rads\]
.
It may be more useful to translate this into seconds of are.
\[2 \pi \: rads = 360 \: degrees = 360 \times 60 \: arcminutes = 360 \times 60^2 \: arcseconds\]
&
Hence to change rads into arcseconds, multiply by  
\[\frac{360 \times 60^2}{2 \pi}\]
.
\[9.76 \times 10^{-5} \: rads = 9.76 \times 10^{-5} \times\frac{360 \times 60^2}{2 \pi}=128.5 \: arcseconds\]
.
For comparison the moon subtends an angle of about 1872 arcseconds.

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