Water has refractive index 1.33. What is the speed of light in water? Use c = 3.0 × 10⁸ m s⁻¹.

Solution & explanation

1. Given n = 1.33 and vacuum speed c = 3.0 × 10⁸ m s⁻¹.

2. Start with refractive index.

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

3. Multiply by v and divide by n.

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

4. Substitute.

   $$v=\frac{300000000}{1.33}$$

5. Divide without rounding n further.

   $$v=225563909.774436$$

6. Round to three significant figures.

v ≈ 2.26 × 10⁸ m s⁻¹