Velocity of Light in a Medium Using µr and εr: Numerical Problems
Physics · Electromagnetic Waves · NEET
The speed of light inside any medium is v = 1/√(µε) = c/√(µr εr), where c = 3 × 10⁸ m/s is the vacuum speed. So the medium always slows light down by the factor √(µr εr), which is exactly the refractive index n. Memory hook: "v = c divided by root mu-r epsilon-r" — bigger √(µr εr) means slower light.
Light slows from c in vacuum to v = c/√(µr εr) in a medium; the slowing factor √(µr εr) is exactly the refractive index n.
Your doubts, answered
Is it v = c × √(µr εr) or v = c / √(µr εr)?
It is v = c / √(µr εr) (divide). Start from v = 1/√(µε). Substitute µ = µ0 µr and ε = ε0 εr, so v = 1/√(µ0 ε0 µr εr) = (1/√(µ0 ε0)) × (1/√(µr εr)) = c / √(µr εr). Since µr and εr are ≥ 1, √(µr εr) ≥ 1, so v is always ≤ c. The multiply option is the NEET trap.
Do I multiply µr and εr, or add them?
Multiply. The formula has the product µr εr inside one square root: √(µr εr). Never add. For µr = 1.0 and εr = 1.44, the product is 1.44, and √1.44 = 1.2. Adding (1.0 + 1.44 = 2.44) gives a wrong √2.44 ≈ 1.56 and a wrong answer.
How do I quickly get v when µr = 1 and εr = 1.44?
Compute √(µr εr) = √(1 × 1.44) = √1.44 = 1.2. Then v = c / 1.2 = (3 × 10⁸) / 1.2 = 2.5 × 10⁸ m/s. This is the exact NEET 2019 answer.
Is √(µr εr) the same as refractive index n?
Yes. Refractive index n = c/v, and since v = c/√(µr εr), you get n = √(µr εr). So once you find √(µr εr) you already have n. For most transparent media µr ≈ 1, so n ≈ √εr.
Why is the speed in a medium always smaller than c?
Because µr ≥ 1 and εr ≥ 1 (εr > 1 for real dielectrics), so the product µr εr ≥ 1 and √(µr εr) ≥ 1. Dividing c by a number that is 1 or more can never make it larger. Light cannot travel faster than c in any ordinary medium.
⚠️ The NEET trap ✗ Using v = c × √(µr εr), which makes light travel faster than c (wrong direction). ✓ v = c / √(µr εr). The medium slows light, so you DIVIDE c by √(µr εr). 🧠 Denser medium = slower light = c on top, √(µr εr) on the bottom.
Real NEET questions
2022
When light propagates through a material medium of relative permittivity εr and relative permeability µr, the velocity of light v is given by (c = velocity of light in vacuum)
A · v = c
B · v = c × √(µr εr)
C · v = √(εr / µr)
D · v = c / √(µr εr) ✓
Solution: Speed in any medium: v = 1/√(µε) = 1/√(µ0 µr ε0 εr). Group the vacuum part: v = (1/√(µ0 ε0)) × (1/√(µr εr)). Since c = 1/√(µ0 ε0), this gives v = c/√(µr εr). Options B (multiply) would make v larger than c, which is impossible.
2019
For a transparent medium the relative permeability and permittivity µr and εr are 1.0 and 1.44 respectively. The velocity of light in this medium would be
A · 2.5 ×10⁸ m/s ✓
B · 3 ×10⁸ m/s
C · 2.08 ×10⁸ m/s
D · 4.32 ×10⁸ m/s
Solution: Step 1: v = c/√(µr εr). Step 2: µr εr = 1.0 × 1.44 = 1.44. Step 3: √1.44 = 1.2. Step 4: v = (3 × 10⁸)/1.2 = 2.5 × 10⁸ m/s. Trap D (4.32 × 10⁸) comes from multiplying instead of dividing.
Solved Electromagnetic Waves NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
