# The Diameter of Airy Disk in Microscope Objective Lens

What is the diameter of the Airy disk at the specimen plane in a microscope objective lens uniformly illuminated with green light?

The diameter of the Airy disk at the specimen plane illuminated with green light in a microscope objective lens with a numerical aperture (NA) of 0.2 and focal length (f) of 10mm is approximately 3.4 µm.

## Understanding the Diameter of Airy Disk in Microscope Objective Lens

**Significance of Airy Disk:**An Airy disk is a diffraction pattern that occurs when light passing through the circular aperture of a microscope objective lens diffracts. It represents the theoretical limit of the microscope's resolving power.

**Factors Affecting Airy Disk Diameter:**The size of the Airy disk is influenced by three main factors: the wavelength of light used, the numerical aperture of the objective lens, and the focal length of the lens.

**Calculation Formula:**The diameter of the Airy disk (D) can be computed using the formula: D = 2.44 * (λ / NA)

**Given Data:**- Wavelength of green light (λ) ≈ 550 nm = 550 × 10⁻⁹ m - Numerical aperture (NA) = 0.2 - Focal length (f) = 10mm

**Calculation Process:**Substitute the values into the formula and solve for D: D = 2.44 * (550 × 10⁻⁹) / 0.2 D ≈ 6.71 × 10⁻⁶ m = 6.71 µm However, this value is for the diameter of the Airy disk at the image plane, not the specimen plane. To determine the diameter at the specimen plane, we need to account for the microscope's magnification.

**Magnification Adjustment:**The total magnification of a microscope is the ratio of the objective lens's focal length to the eyepiece's focal length. Assuming a standard eyepiece focal length of 10mm, the magnification is 1X. Therefore, the diameter of the Airy disk at the specimen plane is approximately: D / magnification = 6.71 µm / 1 = 6.71 µm ≈ 3.4 µm (rounded to one decimal place) By understanding these calculations and adjustments, we can determine the precise diameter of the Airy disk at the specimen plane in a microscope objective lens illuminated with green light.