Light speed in water is 2.25×10⁸ m s⁻¹. Calculate water’s refractive index, taking c = 3.0×10⁸ m s⁻¹.

Solution & explanation

1. Given: v = 2.25×10⁸ m s⁻¹; c = 3.0×10⁸ m s⁻¹.

2. Find: n.

3. Use the speed ratio.

   $$n=\frac{c}{v}$$

4. Substitute both speeds.

   $$n=\frac{300000000}{2.25\times {10}^8}$$

5. Cancel the common power 10⁸.

   $$n=\frac{3}{2.25}=\frac{4}{3}$$

6. State the result with units: n ≈ 1.33, no unit.

n ≈ 1.33