Refractive Index and Dielectric Constant
The refractive index is n = c/v. For a homogeneous linear medium, n = sqrt(mu_r epsilon_r); when mu_r is approximately one, n is approximately sqrt(epsilon_r).
Why this shows up in the exam
Converting measured speed to refractive index · Finding dielectric constant of a non-magnetic medium · Comparing optical density of materials
Learn the idea
Refractive index measures how much a medium reduces wave speed relative to vacuum. If light travels at one-fifth of c in a medium, its refractive index is five. For a non-magnetic medium, the dielectric constant is then the square of that index.
🧠 Memory hook: Index is vacuum speed divided by medium speed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- n = c/v — definition of refractive index
- n = sqrt(mu_r epsilon_r) — material-parameter relation
- epsilon_r = n² — non-magnetic-medium result when mu_r = 1
How to approach it
- 1Find v from the phase or given speed
- 2Calculate n = c/v
- 3Use n squared = mu_r epsilon_r to isolate the requested parameter
Common slip-ups that cost marks
- •Using n = v/c
- •Assuming epsilon_r = n without squaring
- •Dropping mu_r when the problem says it is not one
🌟 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.
An electromagnetic wave in vacuum has wavelength 1 m. Take c = 3 x 10^8 m/s. Find its frequency in units of 10^8 Hz.
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