A single slit of width 0.0300 mm is used to produce a diffraction pattern of 500 nm light on a screen at a distance of 2.00 m from the slit. What angle does the central maximum subtend as measured from the slit?
A) 1.91°
B) 3.82°
C) 0.945°
D) 1.50°
E) 3.00°

Question

Quizplus · Accepted Answer

The angle for the central maximum in a single-slit diffraction pattern can be found using the formula for the first minimum, $ \theta = \sin^{-1}(\frac{\lambda}{w}) $, where $ \lambda $ is the wavelength of the light (500 nm or $ 5 \times 10^{-7} $ m) and $ w $ is the width of the slit (0.0300 mm or $ 3 \times 10^{-4} $ m). The angle to the first minimum gives an idea of the angle subtended by the central maximum. Plugging in the values, $ \theta = \sin^{-1}(\frac{5 \times 10^{-7}}{3 \times 10^{-4}}) \approx \sin^{-1}(0.0016667) \approx 0.0956 $ radians, which converts to about 1.91 degrees when converted to degrees.

A Single Slit of Width 0