Ray Optics (Snell's Law, T.I.R)

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Ray Optics (Snell's Law, T.I.R) is the third lecture within the Waves and Optics section of PH1011. It covers Snell's Law, refractive indexes, and reflection.

Refraction, Reflection
Reflection refers to an incident ray of light hitting off a material boundary and rebounding at an angle equal to that of incidence, reflected in the normal. Refraction refers to light passing through the boundary and being bent (toward the normal when passing into a more dense medium, eg from air to water); in most situations both refraction and reflection occur, splitting an oncoming ray of light into minor components. This occurs at smooth material boundaries; each material has an associated refractive index which determines how much the angle is bent, with nvacuum at 1 and all other materials >1. Refraction must be practically considered with monochromatic light, as different wavelengths refract to different levels (blue bends the most and red bends the least).

Snell's Law
n1sinθ1 = n2sinθ2; the refractive index of a material multiplied by the sine of its angle will be equal on the other side of the boundary. The refractive index of a material is determined by the speed of light in the material; v=c/n. This gives air an index of close to 1, and refractive index as a value has no units. The bending of light occurs as one side of a wave incoming at an angle will slow before the other side, which will skew it. The change in speed occurs due to the fact that molecules have associated kinetic energy; even in a solid they do vibrate, and this oscillation radiates further light. The radiated light interferes with the incoming beam, causing a resultant beam with the same frequency but a lower wavelength and lower speed. Δf/f = Δλ/λ.

Total Internal Reflection
Total internal reflection occurs when light is incident at an angle less than the critical angle (where light is refracted perpendicular to the normal; sinθc = nr/ni; derived as sin90 = 1). This is what allows fibreoptic cables to function.

Summary
Reflection occurs when incident light rebounds back into the medium where it has come from; refraction occurs when it bends toward the normal in a denser medium. Snell's law equates angles and refractive indexes and refraction into a dense medium causes light to slow down, with slight change in wavelength. TIR occurs when light is incident at anything less than the critical angle.