Question

Write down two necessary conditions for interference of light.

Hint:

The word \textbf{coherent} is the key to interference. If you are asked for one condition, this is the one to state. It encapsulates both the same frequency and a constant phase difference.

Answer 1

Step 1: Understanding the Concept:
Interference is a phenomenon in which two or more waves superpose to form a resultant wave of greater, lower, or the same amplitude. For the interference pattern to be stable and observable (a "sustained" interference pattern), certain conditions must be met by the interfering light sources.
Step 2: Detailed Explanation of Conditions:
1. Coherence:
This is the most critical condition. The sources must be coherent. Coherence means two things:
a) Same Frequency/Wavelength: The waves emitted by the sources must have the same frequency. If the frequencies are different, the phase relationship between the waves will change rapidly and randomly, and a stable interference pattern will not be formed.
b) Constant Phase Difference: The phase difference between the waves from the two sources at any point must remain constant over time. If the phase difference changes randomly, the positions of maximum and minimum intensity will also shift randomly, and the pattern will be washed out. This is why two independent light sources (like two light bulbs) cannot produce a visible interference pattern; their phase relationship is not constant. Coherent sources are typically derived from a single parent source (e.g., in Young's double-slit experiment).
2. Same Amplitude (for good contrast):
For the interference pattern to be easily visible, the dark fringes should be perfectly dark, and the bright fringes should be very bright. This happens when the amplitudes of the interfering waves are equal or nearly equal.
- At a point of destructive interference, the resultant intensity is \(I_{min} \propto (A_1 - A_2)^2\). If \(A_1 = A_2\), then \(I_{min} = 0\) (perfectly dark).
- At a point of constructive interference, the resultant intensity is \(I_{max} \propto (A_1 + A_2)^2\).
If the amplitudes are very different, \(I_{min}\) will not be zero, and the contrast between bright and dark fringes will be poor.
Other important conditions include that the sources should be narrow (point sources) and close to each other.
Step 3: Final Answer:
The two most essential conditions for producing a sustained and clear interference pattern are that the sources must be coherent and should have comparable amplitudes.