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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.

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