3.3.2.3
The critical angle is where the refracted ray runs along the boundary
Refraction & Total Internal Reflection — AQA A-Level Physics
Key Definition
Critical angle — The angle of incidence in the denser medium at which the angle of refraction is exactly 90 degrees. The refracted ray travels along the boundary.
$$\sin c = \frac{n_2}{n_1}$$
$$\sin \theta_c = \frac{n_2}{n_1}$$
- $\theta_c$: critical angleThe angle of incidence at which the refracted ray travels along the boundary (angle of refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. = 90 degrees). For angles greater than this, total internal reflection occurs. (degrees)
- $n_1$: 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 the denser medium
- $n_2$: 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 the less dense medium
- The critical angle only exists when light travels from a denser medium into a less dense medium ($n_1 > n_2$).
- The larger 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 denser medium, the smaller the critical angleThe angle of incidence at which the refracted ray travels along the boundary (angle of refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. = 90 degrees). For angles greater than this, total internal reflection occurs..
- For glass (n = 1.5) to air (n = 1): $\theta_c = \sin^{-1}(1/1.5) = 41.8^{\circ}$.
- When the angle of incidence equals the critical angleThe angle of incidence at which the refracted ray travels along the boundary (angle of refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. = 90 degrees). For angles greater than this, total internal reflection occurs., the refracted ray goes along the boundary (90 degrees).
- When the angle of incidence is less than the critical angle, the ray refracts and exits.
- When the angle of incidence exceeds the critical angle, total internal reflectionThe complete reflection of a wave at a boundary when the angle of incidence exceeds the critical angle and the wave travels from a denser to a less dense medium. occurs.
Related:Diffraction