Light of wavelength $687 \mathrm {~nm}$ passes through a single slit that is $0.75 \mathrm {~mm}$ wide. At what distance from the slit should a screen be placed so that the second dark fringe in the diffraction pattern is to be $1.7 \mathrm {~mm}$ from the center of the pattern?

Question

Quizplus · Accepted Answer

The position of the dark fringes in a single-slit diffraction pattern is given by $y = \frac{m\lambda L}{a}$, where $y$ is the distance from the center of the pattern to the fringe on the screen, $m$ is the order of the fringe (with $m = 1$ for the first dark fringe, $m = 2$ for the second, etc.), $\lambda$ is the wavelength of the light, $L$ is the distance from the slit to the screen, and $a$ is the width of the slit. Rearranging this formula to solve for $L$, we get $L = \frac{ya}{m\lambda}$. Substituting the given values ($y = 1.7 \times 10^{-3} \mathrm{m}$, $a = 0.75 \times 10^{-3} \mathrm{m}$, $m = 2$, and $\lambda = 687 \times 10^{-9} \mathrm{m}$), we find $L \approx 0.93 \mathrm{m}$.

Light of Wavelength 687 nm687 \mathrm {~nm}687 nm Passes Through a Single Slit That Is

Light of Wavelength $687 \mathrm {~nm}$ Passes Through a Single Slit That Is