Fresh water has an index of refraction of 1.333. Taking the vacuum speed of light as 3.00 x 10^8 m/s, what is the speed of light in fresh water?
A2.25 x 10^8 m/s
B4.00 x 10^8 m/s
C1.33 x 10^8 m/s
D3.00 x 10^8 m/s
Answer & Solution
Correct answer: A. 2.25 x 10^8 m/s
1. The speed of light through matter is less than in a vacuum because light interacts with the atoms of the material.
2. Rearranging n = c divided by v gives v = c divided by n.
3. Substituting with units, v = (3.00 x 10^8 m/s) divided by 1.333 = 2.25 x 10^8 m/s.
4. The answer is smaller than the vacuum value, as it must be for any material.
5. The 4.00 x 10^8 m/s option comes from multiplying by n, which would put light above its vacuum speed.
_Source: OpenStax College Physics (CC BY 4.0), Ch 25 "Geometric Optics", section 25.3 The Law of Refraction_
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