A Fraunhofer diffraction pattern is produced from a light source of wavelength 460 nm.The light goes through a single slit and onto a screen 0.9 m away.The first dark fringe is 4.5 mm from the central bright fringe.What is the slit width? (1 nm = 10−⁹ m) A)1.8E-4 m B)9.2E-5 m C)3.1E-5 m D)1.4E-4 m E)2.0E-2 m

Question

Quizplus · Accepted Answer

The width of the slit ($a$) in a single-slit diffraction pattern can be calculated using the formula for the position of the first minimum ($y$) given by $y = \frac{\lambda L}{a}$, where $\lambda$ is the wavelength of the light, $L$ is the distance from the slit to the screen, and $y$ is the distance from the central maximum to the first minimum (dark fringe). Rearranging the formula to solve for $a$, we get $a = \frac{\lambda L}{y}$. Substituting the given values ($\lambda = 460 \times 10^{-9}$ m, $L = 0.9$ m, and $y = 4.5 \times 10^{-3}$ m), we find $a = \frac{460 \times 10^{-9} \times 0.9}{4.5 \times 10^{-3}} = 9.2 \times 10^{-5}$ m.

A Fraunhofer Diffraction Pattern Is Produced from a Light Source