The semi vertical angle of the cone of the rays of light incident on the objective of a microscope is `20^(@)`. If the wavelength of incident light is `6000Å`, calculate the smallest distance between two points which can be just resolved.

Explanation

Data: `i_("max") = 20^(@), lambda= 6 xx 10^(-7)m, n=1` (air)
Numerical aperture, `NA=nsini_("max")= 1xx sin20^(@) = 0.34420`
The limit of resolution (for illuminated objects),
`d_("min") = lambda/(2NA) = (6 xx 10^(-7))/(2 xx 0.3420) = 8.772 xx 10^(-7)`m
The limit of resolution (for self-luminous objects),
`d_("min") = (1.22lambda)/(2NA) = 1.22 xx 8.772 xx 10^(-7) = 1.053 xx 10^(-6)`m