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 fringe) in a diffraction pattern is given by $D = 2L \tan(\theta)$, where $L$ is the distance to the screen, and $\theta$ is the angle to the first dark fringe. For small angles, $\tan(\theta) \approx \sin(\theta) = \frac{\lambda}{d}$, where $\lambda$ is the wavelength of light, and $d$ is the diameter of the aperture. Rearranging for $d$, we get $d = \frac{\lambda L}{D/2}$. Substituting $\lambda = 633 \times 10^{-9} m$, $L = 4.0 m$, and $D = 5.4 \times 10^{-2} m$, we find $d \approx 110 \times 10^{-6} m$ or 110 μm.

Light of Wavelength 633 Nm from a He-Ne Laser Passes