Explanation

The minimum angle of resolution (θ) for a lens of diameter (D) and light of wavelength (λ) passing through it can be expressed as:

𝜃= 1.22 𝜆 / 𝐷​

Where:

𝜆 is the wavelength of light

𝐷 is the diameter of the lens

The resolution power (R) is defined as the reciprocal of the angle of resolution:

𝑅 = 1 / 𝜃

Substituting the expression for 𝜃 into the equation for resolution power (R):

𝑅 = 1 / 1.22  𝜆 / 𝐷

Simplifying this expression:

𝑅 = 𝐷 / 1.22 𝜆 

So, the formula for the relation between resolution power (R) and the diameter of the lens (D) is:

𝑅 = 𝐷 / 1.22 𝜆