3.3.2.3
Snell's law relates angles and refractive indices at a boundary
Refraction & Total Internal Reflection — AQA A-Level Physics
$$n_1 \sin \theta_1 = n_2 \sin \theta_2$$
- $n_1$: refractive indexThe ratio of the speed of light in a vacuum to the speed of light in a medium. Determines how much light bends on entering the medium. of material 1
- $n_2$: refractive indexThe ratio of the speed of light in a vacuum to the speed of light in a medium. Determines how much light bends on entering the medium. of material 2
- $\theta_1$: angle of incidence in material 1 (degrees)
- $\theta_2$: angle of refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. in material 2 (degrees)
- Angles are always measured from the normal (the line perpendicular to the boundary).
- Material 1 is the medium the ray enters from. Material 2 is the medium the ray enters into.
- If the ray enters a denser medium ($n_2 > n_1$), it bends towards the normal ($\theta_2 < \theta_1$).
- If the ray enters a less dense medium ($n_2 < n_1$), it bends away from the normal ($\theta_2 > \theta_1$).
Worked Example
A light ray enters a glass cube from air. The angle of incidence is 39 degrees and the angle of refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. is 25 degrees. Show that the refractive indexThe ratio of the speed of light in a vacuum to the speed of light in a medium. Determines how much light bends on entering the medium. of the glass is about 1.5.
Show Solution
1
List known values
- $n_1 = 1$ (air)
- $\theta_1 = 39^{\circ}$
- $\theta_2 = 25^{\circ}$
2
Rearrange Snell's law
$$n_2 = \frac{n_1 \sin \theta_1}{\sin \theta_2} = \frac{\sin 39^{\circ}}{\sin 25^{\circ}}$$
3
Calculate
$$n_2 = \frac{0.6293}{0.4226} = 1.489 = 1.5 \text{ (2 s.f.)}$$
Answer
$n_{\text{glass}} = 1.5$
Common Mistake
MEDIUM
Students often: Measuring the angle from the boundary surface instead of from the normal.
Instead: The angle of incidence and refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. are always measured from the normal (the line at 90 degrees to the boundary). If you are given the angle to the surface, subtract it from 90 degrees.
Instead: The angle of incidence and refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. are always measured from the normal (the line at 90 degrees to the boundary). If you are given the angle to the surface, subtract it from 90 degrees.
Examiner Tips and Tricks
- In a 'show that' question, give your answer to at least one more significant figure than the value given.
- Also check your calculator is in degrees mode, not radians.
Related:Diffraction