Question

A laser produces light of wavelength lamda and amplitude A. The light is directed through two slits that are separated by a small distance. On the other side of the slits is an interference pattern of alternating dark (black) and bright bands. What is the maximum amplitude of the waves in the interference pattern, and where does the maximum amplitude occur?

A) 2A, in the bright bands

B) A, in the bright bands

C) A, in the dark bands

D) 0.5A, in the bright bands

Answer 1

Since the light is directed through two slits, we consider them to be two individual light sources with amplitude A and wavelength $\lambda$ .

Now, when two waves interact, they cause an interference pattern to form. This interference is of two types, constructive and destructive. Constructive interference occurs when one wave's crest or trough interferes with the other wave's crest or trough respectively while destructive interference occurs when a wave's crest interacts with the other's trough and vice versa.

So, constructive interference causes two waves to combine and become stronger and destructive causes them to nullify each other.

So the maximum amplitude of the waves will occur when the two waves undergo constructive interference at their respective amplitudes.

A_max = A + A = 2A

Constructive interference is also what leads to the bright bands (more light). So the maximum amplitude shall occur in the bright bands.

Ans. A) 2A, in the bright bands.