Calculating the Diameter of a Circular Aperture

When light from a He-Ne laser with a wavelength of 633 nm passes through a circular aperture, and is observed on a screen 4.0 m behind the aperture, we can calculate the diameter of the hole.

Calculation Process:

Given data:

• Wavelength (λ) = 633 nm = 633 × 10⁻⁹ m
• Distance to screen (L) = 4.0 m
• Width of central maximum (D) = 1.1 cm

We first need to find half the width of the central maximum, denoted as Y = D / 2 = 1.1 / 2 = 0.55 cm.

Next, we can use the formula for the diameter of the aperture:

α = 1.22λ / (Y / L)

Substitute the given values into the formula:

α = (1.22 × (633 × 10⁻⁹ m)) / (0.55 / 4.0)

α = 0.00000077226 / 0.1375

α = 5.6164 × 10⁻⁶ m

α = (5.6164 × 10⁻⁶ × 10⁶) μm

Therefore, the diameter of the hole is 5.6164 μm