What is the resolution limit set by the size of the objective lens (that is, by diffraction)? Use λ=560nm .

θ = 6.832 / a 10⁻⁷ rad

a= 1 mm,  θ = 6.832 10⁻⁴ rad

Explanation:

The limit of the resolution of a system is given by the first zero of the diffraction pattern for a slit is

                a sin θ = m λ

m = 1

               a sin θ = λ

               sin θ = λ / a

in the case of circular tightness it must be solved in polar coordinates giving

                 sin θ = 1.22 λ / a

as in diffraction experiments the angles are very small we can approximate the sine to the angle, in radians

                 θ = 1.22 λ / a

Let's calculate

                θ = 1.22 560 10⁻⁹ / a

                θ = 6.832 / a 10⁻⁷ rad

In order to finish the calculation, the diameter of the objective lens is needed, for a sample let's use a diameter 1 mm = 10⁻³ m

                 θ = 6.832 10⁻⁴ rad

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