Physics · Electromagnetic Waves · NEET
Yes, they are the same rule for two different media. c = 1/√(µ0ε0) is the speed in vacuum, where µ0 and ε0 are the vacuum values. In any other medium you replace them by the medium's own µ = µ0 µr and ε = ε0 εr, giving v = 1/√(µε). Substituting: v = 1/√(µ0µr ε0εr) = (1/√(µ0ε0)) × 1/√(µr εr) = c/√(µr εr). So the vacuum formula is the special case where µr = εr = 1.
In a medium the atoms have charges that respond to the wave's electric field. This response is measured by εr (and µr for magnetic response), both of which are larger than 1 in matter. A larger εr means the medium stores more electric energy per field, which effectively increases the 'inertia' the wave feels. Since v = c/√(µr εr) and √(µr εr) > 1, the speed v comes out less than c. In vacuum there is nothing to respond, so µr = εr = 1 and the wave moves at the maximum speed c.
µ (mu, absolute permeability) has units and equals µ0 µr. µr (relative permeability) is a pure number with no units. The full formula v = 1/√(µε) uses the absolute values µ and ε. The handy exam form v = c/√(µr εr) uses only the relative numbers, which is why NEET usually gives you µr and εr directly. Never mix them up: if the question gives µr = 1.0, the absolute µ is µ0 × 1.0, not 1.0.
It is division: v = c/√(µr εr). Because µr εr is always at least 1 for real media, dividing makes v smaller than c, which is physically correct (light cannot exceed c). If you accidentally multiply, you get a speed larger than c, which is impossible. This sign of the operation is the most common trap in NEET, so always check that your final v is less than 3×10⁸ m/s.
Refractive index is defined as n = c/v. Putting v = c/√(µr εr) gives n = c ÷ (c/√(µr εr)) = √(µr εr). So the same medium data (µr and εr) gives both the speed and the refractive index. For most transparent, non-magnetic media µr ≈ 1, so n ≈ √εr. This link is covered in detail in refractive index from µr and εr.
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:
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):
Try the real previous-year questions from this chapter — each with the answer and a full solution.
v = 1/√(µε), where µ is the absolute permeability and ε the absolute permittivity of the medium. In terms of relative values it is v = c/√(µr εr).
Because µ = µ0 µr and ε = ε0 εr with µr, εr ≥ 1 for real media. So √(µε) > √(µ0 ε0), which makes v = 1/√(µε) smaller than c = 1/√(µ0 ε0).
Most optical media are non-magnetic, so µr ≈ 1. Then v ≈ c/√εr and the refractive index n = √εr. This is why n is often estimated from the dielectric constant.
No. Frequency is fixed by the source. When speed drops to v, the wavelength shrinks to λ_medium = v/f, but f stays the same as in vacuum.
c = 1/√(µ0ε0) ≈ 3×10⁸ m/s uses only vacuum constants and is the maximum possible speed. v = 1/√(µε) uses the medium's constants and is always smaller.
