Physics · Electromagnetic Waves · NEET
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).
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.
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'.
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.
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.
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
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
Try the real previous-year questions from this chapter — each with the answer and a full solution.
n = √(µr εr), where µr is relative permeability and εr is relative permittivity (dielectric constant). It is a pure number with no units.
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.
Because most optical materials are non-magnetic, so µr ≈ 1. Then n = √(1 × εr) = √εr. This is a special case, not the general rule.
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.
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.
