Due to the dual wave/particle nature of light diffraction occurs with any circular aperture.
After a lot of Calculus using the Bessel function and Fourier transform, the radius of the diffraction disk in angular units can be estimated from the equation:
Sin(theta) = 1.22 x wavelength of the light/D (diameter of the aperture). As you can see the diffraction disk is smaller (which is good) as the wavelength of the light you are observing becomes shorter and is smaller still (also good) as the aperture gets larger.
To find the size of the diffraction disk you divide the wavelength of the light in meters by the aperture in meters and multiply the result by dimensionless constant 1.22. You then take the arcsine of that number and obtain an angle in radians. This can be done on any scientific calculator. Deriving this equation for you would result in a very lengthy post and I do not know if CN supports Calculus notation.