Circular aperture: Light of wavelength 633 nm from a He-Ne laser passes through a circular aperture and is observed on a screen 4.0 m behind the aperture. The diameter of the central bright area is 5.4 cm. What is the diameter of the aperture?
A) 110 μm
B) 2.0 μm
C) 6600 μm
D) 960 μm

Question

Quizplus · Accepted Answer

The diameter of the central bright area (first dark ring) in the diffraction pattern from a circular aperture is given by the formula $D = 2.44 \lambda \frac{L}{d}$, where $D$ is the diameter of the central bright area, $\lambda$ is the wavelength of the light, $L$ is the distance to the screen, and $d$ is the diameter of the aperture. Rearranging this formula to solve for $d$, we get $d = 2.44 \lambda \frac{L}{D}$. Plugging in the given values ($\lambda = 633 \times 10^{-9}$ m, $L = 4.0$ m, and $D = 5.4 \times 10^{-2}$ m), we find $d \approx 110 \times 10^{-6}$ m, or 110 μm.

Circular Aperture: Light of Wavelength 633 Nm from a He-Ne