The resolution of a microscope is diffraction limited, just as the eye, but gain

Question

The resolution of a microscope is diffraction limited, just as the eye, but gains a significant advantage because an object can be placed very close to its objective lens. The smallest resolvable linear separation x_m for an ordinary light microscope is:
x_m=lamda/(2*n*sin (theta))
where lamda is the wavelength of light used, and theta is the half viewing angle of the objective. The quantity 'n*sin(theta) ' is called the numerical aperture of the objective, where n is the index of refraction. The minimum resolvable separation of two objects can be reduced by placing a liquid with a large index of refraction between the object and the objective, as in an oil immersion microscope.

Question:

With light of wavelength 500 nm and a lens with a numerical aperture of 0.43, what is the minimum resolvable separation of two objects?

___________________ micrometers

Explanation / Answer

Just plug in the value. x_m=lamda/2*numerical aperture x_m=500e-9/2*0.43=0.6(micrometer)

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