n identical light waves each of intensity I are superposed in a homogeneous medium. The resultant intensity in their incoherent and coherent addition are respectively (1)zero and n^2 I(2)n I and n^2 I(3)n I and zero(4)n^2 I and n^2 I

Let's delve into the fascinating world of wave interference to address your question regarding the resultant intensity when identical light waves are superposed both incoherently and coherently. The behavior of these waves can vary significantly based on their phase relationship, which leads to different outcomes in terms of intensity.

Understanding Coherent and Incoherent Addition

When we talk about superposing light waves, we need to consider two types of addition: coherent and incoherent.

Coherent Addition

In coherent addition, the waves have a constant phase difference and their frequencies are identical. When n identical light waves, each with intensity I, interfere coherently, the resultant intensity can be calculated using the following formula:

• Resultant Intensity (I_resultant) = n² I

This means that if you have n waves, the intensity multiplies by n squared. For instance, if you have 3 waves each with an intensity of 1 unit, the total intensity would be:

• I_resultant = 3² * 1 = 9 units

Incoherent Addition

On the other hand, incoherent addition occurs when the light waves are not in phase and do not have a consistent phase relationship. In this case, the waves simply add up their intensities without any interference effects.

• Resultant Intensity (I_resultant) = n I

So if you have the same 3 waves, the total intensity would be:

• I_resultant = 3 * 1 = 3 units

Choosing the Correct Option

With this understanding, let’s analyze the options you provided:

• (1) zero and n² I
• (2) n I and n² I
• (3) n I and zero
• (4) n² I and n² I

From our explanation, the coherent addition yields n² I, and the incoherent addition gives us n I. Thus, the correct answer is:

(2) n I and n² I

Final Thoughts

The distinction between coherent and incoherent addition of light waves is fundamental in understanding various optical phenomena, including interference and diffraction. This concept is widely applicable in fields such as telecommunications, optical engineering, and even in the study of quantum mechanics. Recognizing how these waves interact allows us to harness their properties for practical applications.