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At room temperature, if the relative permittivity of water is 80 and the relative permeability is 0.0222, then the velocity of light in water is ______ m s⁻¹.

Asked in GSEB Board March 2018 · Speed in vacuum and in a medium

• (1) 3×10⁻⁸
• (2) 2.5×10⁸
• (3) 2.25×10⁸
• (4) 3.5×10⁸

Step-by-step solution

Why the other options are wrong

• (1) 3×10⁻⁸ is the speed of light with the sign of the exponent flipped -- about 30 nm per second. Asking whether the number is anywhere near 3×10⁸ catches this at once.
• (2) No single slip produces 2.5×10⁸: it answers to a refractive index of 1.2, whereas √μᵣεᵣ = √80×0.0222 = 1.33. Sanity check: 3×10⁸/1.33 = 2.25×10⁸.
• (4) 3.5×10⁸ is faster than light in vacuum. No ordinary medium can do that, because n = √μᵣεᵣ ≥ 1; entering matter always slows the wave.

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