Coherent and Incoherent Sources
Sources are coherent when they emit waves of the same frequency with a time-independent phase difference. Incoherent sources have a fluctuating phase relation, so their cross term averages to zero over the detector response time.
Why this shows up in the exam
Interferometers · Coherent optical communication · Laser metrology
Learn the idea
Stable fringes require sources with a constant phase difference and the same frequency. Two singers holding a steady beat relation can create a fixed loud-soft pattern; unrelated singers drift, so their patterns wash out when averaged.
🧠 Memory hook: Same color is not enough; phase must stay locked.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- I_coherent = I1 + I2 + 2 sqrt(I1 I2) cos(phi) — intensity when phase relation is stable
- <I_incoherent> = I1 + I2 — time-averaged intensity for unrelated sources
How to approach it
- 1Check frequency equality
- 2Check whether phase difference is stable
- 3If not coherent, add intensities only
Common slip-ups that cost marks
- •Treating two separate lamps as coherent
- •Assuming different frequencies form stationary fringes
- •Adding amplitudes for incoherent sources
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A real object is placed 30 cm from a converging lens of focal length 10 cm. Find the real image distance.
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