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Chapter 32: Problem 6

In deriving the intensity in double-slit interference, why can't you simply add the intensities from the two slits?

Short Answer

Expert verified
You can't simply add the intensities from the two slits because the final intensity at every point on the screen is determined by the type of interference occurring at that point - constructive or destructive - and not by the direct sum of the intensities of the individual slits.

Step by step solution

01

Understand Wave Superposition and Interference

According to the superposition principle, when two or more waves overlap, the resultant wave is the algebraic sum of the individual waves. In the context of light or any other wave phenomena, this summing up of waves is known as interference.
02

Understand Constructive and Destructive Interference

When two waves are in phase or the phase difference between them is an even multiple of \(\pi\), they interfere constructively resulting in a wave of greater amplitude. On the other hand, when the waves are out of phase or their phase difference is an odd multiple of \(\pi\), they interfere destructively resulting in waves of lesser amplitude.
03

Relate Interference to Intensity of Waves

The intensity of a wave is directly proportional to the square of its amplitude. If two identical waves interfere constructively, the amplitude of the resultant wave doubles, and the intensity becomes four times. If they interfere destructively, the amplitude of the resultant wave becomes zero and so does the intensity.
04

Apply the above understanding to the Double-slit Experiment

In a double-slit experiment, light from two slits interferes to produce an interference pattern of dark and bright fringes on a screen. The intensity at these different points on the screen is not merely the sum of the intensities from the two slits. Instead, it is determined by the type of interference (constructive or destructive) happening at that particular point.

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