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The speed of light in diamond is 125,000 km s-1. What is the refractive index? (Speed of light in air = 3 x 108 m s-1).

Refraction Plane Surfaces

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Answer

As we know,

μ=Speed of light in vacuum or air (c) Speed of light in diamond (V)μ = \dfrac{\text{Speed of light in vacuum or air (c) }}{\text {Speed of light in diamond (V)}} \\[0.5em]

Given,

Speed of light in diamond = 125,000 km s-1 = 125 x 106 m/s

Speed of light in air, c = 3 × 108 ms-1

Substituting the values in the formula above we get,

μ=3×108125×106μ=3×102125μ=300125⇒μ=2.4μ = \dfrac{3 \times 10^8 }{125 \times 10^6} \\[0.5em] μ = \dfrac{3 \times 10^2}{125} \\[0.5em] μ = \dfrac{300}{125} \\[0.5em] \Rightarrow μ = 2.4 \\[0.5em]

Hence, refractive index = 2.4

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