Coherence is essential for observable interference

Steps:

• Interference patterns require light waves to maintain a constant phase relationship over time.
• Monochromatic light from a single source, like a laser, is coherent and produces clear fringes.
• Light from separate lamps originates from independent atomic emissions with random phases.
• This randomness causes phases to drift, averaging out interference to invisibility.

Why C is correct:

• Coherence means stable phase difference; incoherent light from different lamps lacks this, preventing sustained interference per wave optics principles.

Why the others are wrong:

• A: Monochromatic beams can have identical frequencies if same color filters are used.
• B: Filament temperatures affect intensity/spectrum but not phase coherence directly.
• D: Monochromatic specifies same wavelength, possible with filters despite source differences.

Final answer: C