Question

Orange light with a wavelength of 590 nm passes through a single slit creates a pattern on a screen located some distance away so that the first dark fringe occurs at an angle of 8.0o What is the width of the slit? (

Answer 1

The equation for the minimums of the difraction on one slit is the following (see https://courses.lumenlearning.com/physics/chapter/27-5-single-slit-diffraction/):

$$D\sin \theta = m\lambda$$

where $D$ is the width of the slit, $m = 1$ is the order of minimum (first dark fringe), $\theta = 8\degree$ is the angle of this minimum, and $\lambda = 590nm = 5.9\times 10^{-7}m$ is the wavelength of the light. Thus, obtain:

$$D = \dfrac{m\lambda}{\sin\theta}\\ D = \dfrac{1\cdot 5.9\times 10^{-7}}{\sin8\degree} \approx 42\times 10^{-7}m = 4.2\mu m$$

Answer. $4.2\mu m$.