A beam of monochromatic light passes through a slit that is 11.0 μm wide.If the first order dark fringe of the resulting diffraction pattern is at an angle of 4.31° away from the centerline,what is the wavelength of light?
A)827 nm
B)301 nm
C)602 nm
D)402 nm
E)201 nm

Question

Quizplus · Accepted Answer

The wavelength of light can be calculated using the formula for the first minimum in a single-slit diffraction pattern, which is $\lambda = a \sin(\theta)$, where $a$ is the slit width and $\theta$ is the angle to the first dark fringe. Given $a = 11.0 \mu m = 11.0 \times 10^{-6} m$ and $\theta = 4.31^\circ$, converting $\theta$ to radians gives $\theta = 4.31 \times (\pi/180)$. Substituting these values into the formula yields $\lambda \approx 827 nm$.

A Beam of Monochromatic Light Passes Through a Slit That