Key Equations
Refraction & Total Internal Reflection — AQA A-Level Physics
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Refractive index
$$n = \frac{c}{c_s}$$
- Where:
- $n$ = refractive index (no units)
- $c$ = speed of light in vacuum (\(3 \times 10^{8}\) m \(s^{-1}\))
- $c_s$ = speed of light in the material (m \(s^{-1}\))
Always greater than 1. Air is treated as n = 1.
Snell's law
$$n_1 \sin \theta_1 = n_2 \sin \theta_2$$
- Where:
- $n_1$ = refractive index of medium 1
- $\theta_1$ = angle of incidence (degrees)
- $n_2$ = refractive index of medium 2
- $\theta_2$ = angle of refraction (degrees)
Angles measured from the normal. Material 1 is where the ray comes from.
Critical angle
$$\sin \theta_c = \frac{n_2}{n_1}$$
- Where:
- $\theta_c$ = critical angle (degrees)
- $n_1$ = refractive index of denser medium
- $n_2$ = refractive index of less dense medium
Derived from Snell's law by setting theta_2 = 90 degrees. Only exists when n1 > n2.