Light travels from air into a liquid with i = 45° and r = 30°. Calculate the liquid’s refractive index.

Solution & explanation

1. Given: n_air ≈ 1; i = 45°; r = 30°.

2. Start with Snell’s law.

   $$\sin \left(i\right)=n\times \sin \left(r\right)$$

3. Divide by sin r.

   $$n=\frac{\sin \left(i\right)}{\sin \left(r\right)}$$

4. Substitute angles in degree mode.

   $$n=\frac{\sin \left(\frac{45\times \pi }{180}\right)}{\sin \left(\frac{30\times \pi }{180}\right)}$$

5. Use sin45° = √2/2 and sin30° = 1/2.

   $$n=\frac{1}{2}\times \sqrt{2}\times \frac{1}{\frac{1}{2}}=\sqrt{2}$$

6. State the result with units: n ≈ 1.414, no unit.

n ≈ 1.414