A ray in air (n₁=1.0) strikes glass (n₂=1.5) at 30°. Find the refraction angle.

Solution & explanation

1. Given: i = 30°; n₁ = 1; n₂ = 1.5.

2. Use Snell’s law; angles are measured from the normal.

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

3. Divide both sides by n₂.

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

4. Substitute and evaluate the sine in degree mode.

   $$\sin \left(r\right)=\frac{\sin \left(\frac{30\times \pi }{180}\right)}{1.5}$$

5. Take inverse sine to obtain r, not merely sin r.

   $$r=\frac{180\times \arcsin \left(\frac{\sin \left(\frac{30\times \pi }{180}\right)}{1.5}\right)}{\pi }$$

6. The angle is approximately 19.4712 degrees.

7. State the result with units: r ≈ 19.47°

r ≈ 19.47°