Two-Wave Superposition and Intensity
For two mutually coherent waves of intensities I1 and I2 with phase difference phi, the time-averaged resultant intensity contains an interference cross term. For equal intensities I0, it reduces to a cosine-squared law.
Why this shows up in the exam
Phase sensing · Optical interferometry · Noise-cancelling wave demonstrations
Learn the idea
Resultant intensity depends on both individual intensities and their phase difference. Two light waves add as electric-field arrows, not as brightness numbers. Depending on their relative phase, the arrows reinforce partly, fully, or oppose.
🧠 Memory hook: Add fields first; intensity comes after squaring.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- I = I1 + I2 + 2 sqrt(I1 I2) cos(phi) — general two-beam interference intensity
- I = 4 I0 cos²(phi/2) — equal individual intensities
- phi = 2 pi Delta/lambda — phase difference from path difference in one medium
How to approach it
- 1Convert path difference to phase
- 2Use the unequal-intensity formula unless equality is stated
- 3Check limiting cases phi = 0 and pi
Common slip-ups that cost marks
- •Adding intensities for coherent beams
- •Using cos(phi/2) instead of its square
- •Forgetting unequal beam amplitudes
🌟 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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