Light of wavelength 687 nm passes through a single slit that is 0.75 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 mm from the center of the pattern?
A)0.39 m
B)0.93 m
C)1.1 m
D)1.5 m
E)1.9 m

Question

Quizplus · Accepted Answer

The position of the dark fringes in a single-slit diffraction pattern can be calculated using the formula $y = \frac{m\lambda L}{a}$, where $y$ is the distance from the center of the pattern to the m-th dark fringe, $\lambda$ is the wavelength of the light, $L$ is the distance from the slit to the screen, $a$ is the width of the slit, and $m$ is the order number of the dark fringe. For the second dark fringe, $m = 2$, $\lambda = 687 \times 10^{-9}$ m (687 nm converted to meters), $a = 0.75 \times 10^{-3}$ m (0.75 mm converted to meters), and $y = 1.7 \times 10^{-3}$ m (1.7 mm converted to meters). Rearranging the formula to solve for $L$, we get $L = \frac{ya}{m\lambda}$. Plugging in the values, $L = \frac{(1.7 \times 10^{-3})(0.75 \times 10^{-3})}{2(687 \times 10^{-9})} \approx 0.93$ meters.

Light of Wavelength 687 Nm Passes Through a Single Slit