An optical microscope is being examined for its ability to distinguish closely spaced points of light.
(i) Define the term numerical aperture for a microscope objective.
(ii) Starting from the criterion for the just–resolved images of two point objects formed by a circular aperture, derive an expression for the minimum distance d between the two points that can be resolved in terms of the wavelength λ of light and the numerical aperture of the objective.
(iii) For light of wavelength 550nm and an objective of numerical aperture 1.25, calculate the minimum distance that can be resolved.
(iv) A second microscope uses light of wavelength 400nm with an objective of numerical aperture 0.85. Which microscope offers the finer resolution? Determine the factor by which their resolving limits differ.