Coherence conditions — requirements for perfectly coherent radiation For two waves to be perfectly coherent (ideal case), which set of conditions applies?

Introduction / Context:
Coherence measures the constancy of phase between waves. In optics and electromagnetics, coherence underpins interference, holography, and many sensing techniques. Perfect coherence is an idealization but helps frame practical requirements for high-contrast interference patterns.

Given Data / Assumptions:

• Idealized “perfect” coherence context.
• Monochromaticity and controlled geometry are considered.
• Polarization matching is implicitly satisfied for high-visibility fringes.

Concept / Approach:

Perfect temporal coherence requires a single frequency (infinite coherence time/length). High spatial coherence requires parallel, collimated beams so that phase across the aperture is predictable. In practice, lasers approximate these conditions; extended sources or finite bandwidths reduce coherence and fringe visibility.

Step-by-Step Solution:

Verification / Alternative check:

Michelson interferometer visibility improves with narrower spectral width and better collimation/alignment, illustrating the role of these conditions.

Why Other Options Are Wrong:

• Selecting any single condition alone does not ensure perfect coherence; the comprehensive set is needed in the ideal case.

Common Pitfalls:

• Overlooking polarization; mismatched polarization reduces interference even with good coherence.
• Confusing collimation with focusing; focused beams can still interfere but complicate phase control.

Final Answer:

All of these.