To understand why two independent monochromatic sources are considered incoherent, we need to delve into the concept of coherence and how it relates to the detection of light intensity. The key factor here is the time it takes for a detector to measure light intensity at a specific position.
Coherence Explained
Coherence refers to the correlation between the phases of waves at different points in space and time. When we talk about two light sources being coherent, it means that their light waves maintain a constant phase relationship. In contrast, incoherent sources do not have this consistent phase relationship, leading to fluctuations in intensity over time.
Time Scale of Detection
The question revolves around the time it takes for a detector to measure light intensity. The time scale of 10-8 seconds is significant because it is related to the temporal coherence of the light sources. For two sources to be considered incoherent, the time required for the detector to register intensity must be:
- Much greater than 10-8 seconds: This means that the detector takes a longer time to average out the fluctuations in intensity caused by the incoherent sources.
- Nearly equal to 10-8 seconds: This would imply that the detector can just keep up with the fluctuations, which does not support the idea of incoherence.
- Much less than 10-8 seconds: If the detector operates on a much shorter time scale, it would not be able to capture the variations in intensity effectively, leading to a misinterpretation of coherence.
Correct Answer
Given this understanding, the correct choice is a) much greater than 10-8 sec. This indicates that the detector requires a longer time to average out the intensity fluctuations caused by the incoherent sources, thus confirming their incoherent nature.
Real-World Analogy
Think of it like trying to listen to two different songs playing at the same time. If you only have a moment to hear them, you might catch snippets of both, but you won't be able to discern the individual melodies clearly. However, if you take your time to listen, you can appreciate how different they are. Similarly, a detector that takes a longer time to measure intensity can better understand the incoherent nature of the light from two independent sources.
In summary, the incoherence of two independent monochromatic sources is fundamentally linked to the time it takes for a detector to accurately measure light intensity, with the requirement being that this time is much greater than 10-8 seconds.
