When a single slit that is $0.050 \mathrm {~mm}$ wide is illuminated by light of $550 - \mathrm { nm }$ wavelength, what is the angular separation between the first two minima on one side of the central maximum?
A) $0.63 ^ { \circ }$
B) $0.54 ^ { \circ }$
C) $0.36 ^ { \circ }$
D) $0.47 ^ { \circ }$
E) $1.3 ^ { \circ }$

Question

Quizplus · Accepted Answer

The angular separation between the first two minima on one side of the central maximum in a single-slit diffraction pattern can be calculated using the formula $\theta = \frac{\lambda}{a}$, where $\lambda$ is the wavelength of the light and $a$ is the width of the slit. Given $\lambda = 550 \, \text{nm} = 550 \times 10^{-9} \, \text{m}$ and $a = 0.050 \, \text{mm} = 0.050 \times 10^{-3} \, \text{m}$, $\theta = \frac{550 \times 10^{-9}}{0.050 \times 10^{-3}} = 0.011$. To convert this to degrees, $\theta = 0.011 \times \frac{180}{\pi} \approx 0.63^\circ$.

When a Single Slit That Is 0.050 mm0.050 \mathrm {~mm}0.050 mm Wide Is Illuminated by Light Of

When a Single Slit That Is $0.050 \mathrm {~mm}$ Wide Is Illuminated by Light Of