Diffraction Limit Calculator

Diffraction Limit Calculator:

Enter the values of  wavelength, w_(m) and  aperture diameter, d_(m) to determine the value of Diffraction Limit, DL_(rad).

Enter Wavelength:		m
Enter Aperture Diameter:		m
Result – Diffration Limit:		rad

Diffraction Limit Formula:

The diffraction limit is the fundamental limit of resolution for an optical system due to the wave nature of light. It defines the smallest detail that can be resolved using a lens, microscope, or telescope. The diffraction of light occurs when it passes through an aperture, such as a lens or the pupil of an eye, causing the light waves to spread and interfere with each other.

This interference forms a diffraction pattern consisting of a central bright region (Airy disk) surrounded by alternating dark and bright rings. The ability to distinguish two closely spaced objects is limited by this pattern, as they merge when they are too close, reducing clarity. The diffraction limit is dependent on both the wavelength of light (w) and the diameter of the aperture (d).

A larger aperture allows for a smaller diffraction limit, improving resolution. Conversely, using shorter wavelengths also enhances resolution. This principle is critical in designing optical instruments such as cameras, telescopes, and microscopes, where achieving the highest possible resolution is essential.

Diffraction Limit, DL_(rad) in radians equals 1.22 times the wavelength, w_(m) in metres divided by the aperture diameter, d_(m) in metres.

Diffraction Limit, DL_(rad) = 1.22 * w_(m) / d_(m)

DL_(rad) = diffration limit in radians, rad.

w_(m) = wavelength in metres, m.

d_(m) = aperture diameter in metres, m.

Diffraction Limit Calculation:

1. Find the diffraction limit of a telescope with an aperture of 2 metres observing light of wavelength 500 nm.
   Given: w_(m) = 500nm = 500 * 10^-9m, d_(m) = 2m.

Diffraction Limit, DL_(rad) = 1.22 * w_(m) / d_(m)

DL_(rad) = 1.22 *  500 * 10^-9 / 2

DL_(rad) = 6.1 * 10^-7 / 2

DL_(rad) = 3.05 * 10^-7 rad.

2. A microscope has a diffraction limit of 1.5 * 10⁻⁷ radians, and the aperture used is 0.8 metres. Find the wavelength of light used.

Given:  DL_(rad) = 1.5 * 10⁻⁷ rad, d_(m) = 0.8m.

Diffraction Limit, DL_(rad) = 1.22 * w_(m) / d_(m)

w_(m) = DL_(rad) * d_(m) / 1.22

w_(m) = 1.5 * 10⁻⁷ * 0.8 / 1.22

w_(m) = 9.84 * 10⁻⁸ m.