Light of wavelength 687 nm is incident on a single slit 0.75 mm wide.At what distance from the slit should a screen be placed if the second dark fringe in the diffraction pattern is to be 1.7 mm from the center of the diffraction pattern?
A) 0.39 m
B) 0.47 m
C) 0.93 m
D) 1.1 m
E) 1.9 m

Question

Quizplus · Accepted Answer

The position of the dark fringes in a single-slit diffraction pattern is given by the formula $y = \frac{m\lambda L}{a}$, where $y$ is the distance from the center of the pattern to the fringe on the screen, $m$ is the order of the fringe (for the second dark fringe, $m = 2$), $\lambda$ is the wavelength of the light (687 nm = $687 \times 10^{-9}$ m), $L$ is the distance from the slit to the screen, and $a$ is the width of the slit (0.75 mm = $0.75 \times 10^{-3}$ m). We are given $y = 1.7$ mm = $1.7 \times 10^{-3}$ m and need to solve for $L$.Rearranging the formula to solve for $L$, we get $L = \frac{ya}{m\lambda}$.Substituting the given values, $L = \frac{(1.7 \times 10^{-3}) \times (0.75 \times 10^{-3})}{2 \times (687 \times 10^{-9})}$.Calculating this gives $L \approx 0.93$ meters, which corresponds to choice C.

Light of Wavelength 687 Nm Is Incident on a Single