Light of wavelength 589 nm is used to view an object under a microscope. The aperature of the objective has a diameter of `0.900 cm`. Find
The limiting angle of resolution.

Explanation

Here `lamda = 589 nm = 589 xx 10^(-9) m`
`a = 0.900 cm = 0.900 xx 10^(-2) m`
`Delta theta = 1.22 (lamda/a) = 1.22 ((589 xx 10^(-9)m)/(0.900 xx 10^(-2)m) ) rad`
` = 7.89 xx 10^(-5) rad `
(b) To obtain the smallest angle corresponding to the maximum limit of resolution, we have to use the shortest wavelength (`lamda` = 400nm) in the visible spectrum.
Limiting angle of resolution
`Delta theta = 1.22 ((400 xx 10^(-9) m)/(0.900 xx 10^(-2) m) ) = rad = 5.42 xx 10^(-5) rad `
(c ) Wavelength of light in water,
`lamda_w = (lamda_a)/(mu) = (589 nm)/(1.33) = 443nm `
`theta = 1.22 ((443 xx 10^(-9)m)/(0.900 xx 10^(-2) m) ) rad = 6.00 xx 10^(-5) rad `
Since `Delta theta ` in this case is less than that in case (a), resolving power increases.