A ray travels from air into water at incidence 40°. Water has refractive index 1.33. Find the refraction angle.

Solution & explanation

1. Take n₁ = 1.00, n₂ = 1.33, i = 40°, measured from the normal.

2. Apply Snell’s law.

   $$n_1\times \sin \left(i\right)=n_2\times \sin \left(r\right)$$

3. Isolate sin r.

   $$\sin \left(r\right)=\frac{n_1\times \sin \left(i\right)}{n_2}$$

4. Substitute the values in degree mode.

   $$\sin \left(r\right)=\frac{\sin \left(\frac{40\times \pi }{180}\right)}{1.33}$$

5. Evaluate the ratio before inverse sine.

   $$\sin \left(r\right)=0.4832989547$$

6. Take inverse sine to obtain the angle, not merely its sine.

   $$r=\frac{180\times \arcsin \left(\frac{\sin \left(\frac{40\times \pi }{180}\right)}{1.33}\right)}{\pi }$$

r ≈ 28.90°