Optical Path and Phase Difference
Optical path length is the line integral of refractive index along a path. For monochromatic vacuum wavelength lambda_0, phase difference equals 2 pi times the optical-path difference divided by lambda_0.
Why this shows up in the exam
Interferometric thickness measurement · Optical coatings · Phase-delay design
Learn the idea
Phase accumulates according to optical path length, not geometric distance alone. A wave cycles more times through a slower optical medium over the same thickness, so equal rulers can produce unequal phases.
🧠 Memory hook: Count cycles with n times distance.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- OPL = integral(n ds) — optical path along a general route
- phi = (2 pi/lambda₀) OPL — phase accumulated relative to vacuum wavelength
- Delta phi = 2 pi Delta/lambda₀ — phase from optical-path difference Delta
- lambda_medium = lambda₀/n — wavelength in a nondispersive medium
How to approach it
- 1Write each path's nL
- 2Subtract optical paths with a sign convention
- 3Convert to phase only at the end
Common slip-ups that cost marks
- •Using geometric path difference through glass
- •Changing frequency on refraction
- •Mixing medium wavelength with vacuum optical path
🌟 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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