Reflection and Refraction

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Reflection. Rope with Free Boundary: pulse is reflected

Rope with Fixed Boundary: pulse is reflected and inverted

4.5.1 Reflection: see diagram to right. The angle of incidence i (angle between the ray and the normal to the reflecting surface at the point of incidence) is equal to the angle of reflection r (angle between normal and reflecting ray).

4.5.2 Refraction. This happens whenever a wave changes its speed going from one medium to another. Frequency always remains constant, so wavelength will also have to change.

Light travels at 300,000,000 m/s (c) in a vacuum and all other media the velocity is smaller. This relationship is responsible for the refraction of light or the change of direction of the ray of light.

Snell's Law: sin(theta 1)/sin(theta 2) = v1/v2 = n2/n1

n represents the index of refraction of a given medium. n = c/cmedium. Indexes of refraction are always greater than one. Why?

 

Calculus Based proof of Snell's Law

4.5.5/61. Interference is a result of how waves interact with each other.

Constructive Interference: a superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave.

Consider two sources. d1 = the distance from point P to source 1. d2 = the distance from point P to source 2.

d1/v - d2/v = nT ... so: d1 - d2 = nTv = n(wavelength) [n = intenger]

path difference is an integral multiple of the wavelength

Destructive Interference: a superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave.

d1 - d2 = (n + 1/2)wavelength [n = integer]

If the path difference is anything other than an integral or half-integral multiple of the wavelength, then: 0 < resultant amplitude < 2A

 

Beats are an example of the effects of interference ...

 

HW. PG 236:1-8, 11.