Problem 14-83 Diffraction - Part 3 - B

A point source emits light of wavelength \(520\; nm\) toward a single slit of width \(0.085\; mm\). The light creates a diffraction pattern on a screen located \(2.2 \;m\) from the screen.

(a) What is the width of the central maximum?
(b) What angle do the first order fringes subtend with the slit?

[Ans. (a) \(2.7 \;cm\)   (b) \(0.70^\circ\)]

Accumulated Solution

Diagram B of the width of the central maximum.

\(\sin \theta = x/L = N \lambda/w \\ N = 1\)

Corrrect!
\(\sin \theta = x/L = 1 \lambda/w \\ x = \frac{\lambda L}{w} = \frac{(520 \times 10^{-9}\; m)(2.2 \; m)}{0.085 \times 10^{-3}\; m} = 135 \times 10^{-2} \;m\)

The width of the central maximum is:

(A)  \(0\)

(B)  \(1.35 \times 10^{-2}\; m = 1.4\; cm\)

(C)  \(2 \times 1.35 \times 10^{-2} \; m = 2.7 \;cm\)