The refractive index of a medium is n = √(µr εr), where µr is the relative permeability and εr is the relative permittivity (dielectric constant) of that medium. It comes from n = c/v, because light slows down to v = c/√(µr εr) inside matter. Memory hook: "n is the square root of the two relatives multiplied" — always multiply µr and εr, then take one square root.
Light travels at c in vacuum and slows to v = c/n in a medium. Dividing the two speeds cancels µ0 and ε0, leaving the refractive index n = √(µr εr) — the product of the two relative constants under a single square root.
Your doubts, answered
Is refractive index the square root of (µr × εr) or just of εr?
It is the square root of the product: n = √(µr εr). Many students remember only n = √εr because most transparent media are non-magnetic, so µr ≈ 1 and √(µr εr) becomes √εr. That shortcut is only true when µr = 1. If NEET gives you a magnetic medium (µr ≠ 1), you MUST multiply both: n = √(µr εr).
Why is there a square root in the refractive index formula?
The speed of light in a medium is v = 1/√(µε), which already has a square root. Refractive index is n = c/v = √(µε)/√(µ0 ε0) = √(µr εr). So the square root is inherited from the wave-speed formula c = 1/√(µ0 ε0). Doubling εr does NOT double n — it multiplies n by √2 only.
What is the difference between n = √(µr εr) and v = c/√(µr εr)?
They are the same physics written two ways. n = √(µr εr) gives the refractive index (a pure number, no units). v = c/√(µr εr) gives the actual speed of light in the medium (in m/s). Since n = c/v, once you find n you get v = c/n. Use n when the question asks 'refractive index', use v when it asks 'velocity of light in the medium'.
Do I add or multiply µr and εr?
Multiply, never add. The formula is n = √(µr × εr). A common wrong answer is √(µr + εr) or µr × εr without the root. For NEET, write the product first, then take the single square root of that product.
Is dielectric constant the same as εr?
Yes. Dielectric constant K and relative permittivity εr are the same quantity for these problems. So if a question says 'dielectric constant is 4', use εr = 4. For a non-magnetic dielectric (µr = 1), n = √(1 × 4) = 2.
⚠️ The NEET trap ✗ Using n = √εr (ignoring µr) even when the medium is magnetic and µr ≠ 1. ✓ Always use n = √(µr εr). For NEET 2023: εr = 2, µr = 1.5, so n = √(2 × 1.5) = √3, not √2. 🧠 NTA loves giving µr ≠ 1 to catch students who memorised only √εr. When you see a µr value that is NOT 1, they are testing exactly this. Multiply both, then one square root.
Real NEET questions
NEET 2023 Phase 2
ε₀ and µ₀ are the electric permittivity and magnetic permeability of free space respectively. If the corresponding quantities of a medium are 2ε₀ and 1.5µ₀ respectively, the refractive index of the medium will nearly be
A · 3
B · 2
C · √2
D · √3 ✓
Solution: Step 1: Read relatives. Medium permittivity = 2ε₀ so εr = 2. Medium permeability = 1.5µ₀ so µr = 1.5. Step 2: Apply n = √(µr εr) = √(1.5 × 2) = √3 ≈ 1.73. Step 3: The trap answer √2 comes from ignoring µr and using only √εr = √2. Correct answer is √3 (option D).
NEET 2019 Odisha
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: Find n = √(µr εr) = √(1.0 × 1.44) = √1.44 = 1.2. Step 2: Use v = c/n = (3 ×10⁸)/1.2 = 2.5 ×10⁸ m/s. Step 3: Notice √1.44 = 1.2 is a clean square root — NEET picks numbers whose root is exact. Answer is 2.5 ×10⁸ m/s (option A).
Solved Electromagnetic Waves NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the formula for refractive index in terms of permeability and permittivity?
n = √(µr εr), where µr is relative permeability and εr is relative permittivity (dielectric constant). It is a pure number with no units.
How is n = √(µr εr) derived?
Speed in vacuum c = 1/√(µ0 ε0) and speed in medium v = 1/√(µ0µr ε0εr). Then n = c/v = √(µr εr). The µ0 and ε0 cancel, leaving only the relative values.
For most transparent materials, why is n ≈ √εr?
Because most optical materials are non-magnetic, so µr ≈ 1. Then n = √(1 × εr) = √εr. This is a special case, not the general rule.
Can refractive index be less than 1 using this formula?
For normal NEET media µr εr > 1, so n > 1. n would be less than 1 only if the product µr εr < 1, which is not tested in standard NEET EM-wave problems.
How do I get the speed of light in the medium after finding n?
Use v = c/n. First compute n = √(µr εr), then divide c = 3 ×10⁸ m/s by n. Example: n = 1.5 gives v = 2 ×10⁸ m/s.
