A light ray passes from air into glass (n = 1.5) at an angle of incidence of 30°. Find the angle of refraction — Physics problems | PhysLabo
Loading...

Angle of refraction of light in glass

Medium 11 grade Optics / Refraction of Light

A light ray passes from air into glass of refractive index $n = 1.5$ at an angle of incidence $\alpha = 30°$. Find the angle of refraction $\beta$.

Given
  • $\alpha = 30°$
  • $n = 1.5$
  • $\beta = ?$
Visual demonstration
Hints
Hint 1 / 2
Law of refraction: $\sin \alpha / \sin \beta = n$.
Hint 2 / 2
$\sin 30° = 0.5$; going into the denser medium the angle decreases, so the answer must be less than 30°.
Solution

The law of refraction (Snell's law):

$$\frac{\sin \alpha}{\sin \beta} = n \Rightarrow \sin \beta = \frac{\sin \alpha}{n}$$

$$\sin \beta = \frac{\sin 30°}{1.5} = \frac{0.5}{1.5} = \frac{1}{3} \approx 0.333$$

$$\beta = \arcsin 0.333 \approx 19.5°$$

Answer

$\beta \approx 19.5°$