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 à 10â»â¹ 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 à (633 à 10â»â¹ m)) / (0.55 / 4.0)
α = 0.00000077226 / 0.1375
α = 5.6164 à 10â»â¶ m
α = (5.6164 à 10â»â¶ à 10â¶) μm
Therefore, the diameter of the hole is 5.6164 μm