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Chapter 25: Problem 6

Two incoherent EM waves of intensities \(9 I_{0}\) and \(16 I_{0}\) travel in the same direction in the same region of space. What is the intensity of EM radiation in this region?

Short Answer

Expert verified
Answer: The intensity of the electromagnetic radiation in the region is \(25 I_{0}\).

Step by step solution

01

Recall the principle of superposition for incoherent waves

For incoherent waves, the intensities of the waves sum up to give the total intensity in the region. This is due to the idea that the energy carried by incoherent waves is unrelated, so their energies just add up.
02

Identify the intensities of the two EM waves

The intensities of the two EM waves are given as \(9 I_{0}\) and \(16 I_{0}\).
03

Add the intensities to find the total intensity

To find the intensity of EM radiation in the region, we add the intensities of the two waves: Total Intensity = \(9 I_{0} + 16 I_{0}\)
04

Simplify the expression

Combine the two terms with the same base (\(I_{0}\)) to find the total intensity: Total Intensity = \((9 + 16) I_{0}\)
05

Calculate the total intensity

Compute the sum inside the parentheses and multiply it by \(I_{0}\): Total Intensity = \(25 I_{0}\) The intensity of the electromagnetic radiation in this region is \(25 I_{0}\).

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Most popular questions from this chapter

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