Theoretical Background
Lenses reconstruct the light scattered by an object. To successfully achieve this end, ideally, all the diffraction orders have to be collected. This is of course related to the opening angle of the lens and its refractive index. The resolution of a microscope is defined as the minimum separation needed between two objects under examination in order for the microscope to discern them as separate objects. This minimum distance is labelled δ. If two objects are separated by a distance shorter than δ, they will appear as a single object in the microscope.
A measure of the resolving power, R.P., of a lens is given by its numerical aperture, NA:
where λ is the wavelength of light. From this it is clear that a good resolution (small δ) is connected with a high numerical aperture.
The numerical aperture of a lens is defined as
where α0 is the angle spanned by the objective lens seen from the sample, and n is the refractive index of the medium between the lens and specimen (≈1 for air).
State of the art objectives can have a numerical aperture of up to 0.95. Because sin α0 is always less than or equal to unity, the numerical aperture can never be greater than unity for an objective lens in air. If the space between the objective lens and the specimen is filled with oil however, the numerical aperture can obtain values greater than unity. This is because oil has a refractive index greater than 1.
Read more about this topic: Oil Immersion
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