Answer to Question #88043 in Optics for Nicholas Legault

Question

Red light with a wavelength of 725 nm shines through a single slit, and forms a pattern on a screen placed 1.25 m away. If the width of the slit is 18.5 micrometers, find the width of the central maximum (a) in degrees and (b) in centimeters.

Answer 1

wavelength $\lambda = 725\, \text{nm}$

Distance from slit to screen $L = 1.25\, \text{m}$

Width of the slit $d = 18.5 \, \mu\text{m}$

Find the angle for the first minimum:

$$d \sin \theta = \lambda$$

It is small, therefore:

$$\sin \theta = \frac{\lambda}{d} \approx \frac{x}{L} \Rightarrow x = \frac{\lambda L}{d}$$

The width of the central maximum :

b)

$$\Delta = 2x = \frac{2\lambda L}{d} = 9.8\, \text{cm}$$

a)

$$2\theta = \frac{2\lambda}{d}\, \text{rad} =\frac{2\lambda}{d} \cdot 180/\pi = 4.5^\circ$$