Chapter 24 - Physics Notes

Refraction: The change in direction of light as it enters a new medium at a nonzero angle due to the light’s speed changing in the new medium.
Index of Refraction (n): The ratio of the speed of light in a vacuum to the speed of light in a medium.
Critical Angle (θ_c): The angle of incidence that will produce an angle of refraction of 90°; beyond this angle, total internal reflection will occur.
Total Internal Reflection: The phenomenon that occurs when light incident on an interface is trying to move from a more optically dense to a less optically dense medium at an angle greater than the critical angle and the ray reflects off the interface instead.
Dispersion: The spreading of light into a spectrum of colors.

Cause of Refraction

Light travels more slowly through matter than through a vacuum.
When light passes into a medium in which its speed is slower, it bends toward the normal line.
When light passes into a medium in which its speed is faster, it bends away from the normal line.
The speed of light in a medium is determined by the medium’s optical density, indicated by the medium’s index of refraction (n).

Snell’s law provides a relationship between the angle of refraction (θ_r) and the angle of incidence (θ_i): n_i sin θ_i = n_r sin θ_r.
θ_i: angle of incidence
θ_r: angle of refraction
n_i: index of refraction of the medium containing the incident ray
n_r: index of refraction of the medium containing the refracted ray

Find the angle of refraction when light traveling in air reaches the interface between air and ethanol at an angle of 36.2°.

n_i = 1.0003

θ_i = 36.2°

n_r = 1.36

θ_r = sin^–1 (n_i sin θ_i / n_r)

θ_r = sin^–1 (1.0003 sin 36.2° / 1.36)

θ_r = 25.7°

As light goes from a more optically dense medium to a less optically dense medium, the light is refracted away from the normal line.
If the angle of incidence increases to the critical angle, the light refracts along the interface.
At angles of incidence greater than the critical angle, total internal reflection occurs.
Mathematically, the critical angle can be solved using: θ_c = sin^–1 (n_r / n_i).

Find the critical angle for a water-air interface.

n_i = 1.333

n_r = 1.0003

θ_c = sin^–1 (n_r / n_i)

θ_c = sin^–1 (1.0003 / 1.333)

θ_c = 48.626°

Different frequencies of visible light have different indexes of refraction in the same materials.
White light can be dispersed into a spectrum of colors.
Examples include traditional optical prisms, atmospheric rainbows, optical illusions, inferior mirage, and superior mirage.