Chapter 35 Serway & Jewett 6th Ed.

How to View Light As a Ray As a Wave As a Particle

What happens to a plane wave passing through an aperture? The limit of geometric (ray) optics, valid for lenses, mirrors, etc. Point Source Generates spherical Waves

{ } y Eo cos (kx - t) Bo E x B Surface of constant phase { } Eo Bo E x B Surface of constant phase For fixed t, when kx = constant z

Index of Refraction 1 n1 = 2 n2

When material absorbs light at a particular frequency, the index of refraction can become smaller than 1!

Reflection and Refraction

Oct. 18, 2004

Fundamental Rules for Reflection and Refraction in the limit of Ray Optics Huygens’s Principle Fermat’s Principle Electromagnetic Wave Boundary Conditions

Huygens’s Principle

Huygens’s Principle All points on a wave front act as new sources for the production of spherical secondary waves k Figure 35.17 Huygens’s construction for (a) a plane wave propagating to the right Fig 35-17a, p.1108

Reflection According to Huygens Incoming ray Outgoing ray Side-Side-Side AA’C   ADC 1 = 1’

Refraction

Figure 35.19 Huygens’s construction for proving Snell’s law of refraction. At the instant that ray 1 strikes the surface, it sends out a Huygens wavelet from A and ray 2 sends out a Huygens wavelet from B. The two wavelets have different radii because they travel in different media. Fig 35-19, p.1109

Show via Huygens’s Principle Snell’s Law v1 = c in medium n1=1 and v2 = c/n2 in medium n2 > 1.

Fundamental Rules for Reflection and Refraction in the limit of Ray Optics Huygens’s Principle Fermat’s Principle Electromagnetic Wave Boundary Conditions

Fermat’s Principle and Reflection A light ray traveling from one fixed point to another will follow a path such that the time required is an extreme point – either a maximum or a minimum.

Figure 35.31 Geometry for deriving Snell’s law of refraction using Fermat’s principle. Fig 35-31, p.1115

Rules for Reflection and Refraction n1 sin 1 = n2 sin 2 Snell’s Law

Optical Path Length (OPL) S P For n = 1.5, OPL is 50% larger than L When n constant, OPL = n  geometric length.

Fermat’s Principle, Revisited A ray of light in going from point S to point P will travel an optical path (OPL) that minimizes the OPL. That is, it is stationary with respect to variations in the OPL.

Fundamental Rules for Reflection and Refraction in the limit of Ray Optics Huygens’s Principle Fermat’s Principle Electromagnetic Wave Boundary Conditions

ki = (ki,x,ki,y) kr = (kr,x,kr,y) kt = (kt,x,kt,y)

Figure 35. 22 White light enters a glass prism at the upper left Figure 35.22 White light enters a glass prism at the upper left. A reflected beam of light comes out of the prism just below the incoming beam. The beam moving toward the lower right shows distinct colors. Different colors are refracted at different angles because the index of refraction of the glass depends on wavelength. Violet light deviates the most; red light deviates the least. Fig 35-22, p.1110

Figure 35.25 (Example 35.7) A light ray passing through a prism at the minimum angle of deviation  min. Fig 35-25, p.1111

Figure 35.24 The formation of a rainbow seen by an observer standing with the Sun behind his back. Fig 35-24, p.1110

Active Figure 35. 23 Path of sunlight through a spherical raindrop Active Figure 35.23 Path of sunlight through a spherical raindrop. Light following this path contributes to the visible rainbow. Fig 35-23, p.1110

Total Internal Reflection

Total Internal Reflection

A bundle of optical fibers is illuminated by a laser.

(Left ) Strands of glass optical fibers are used to carry voice, video, and data signals in telecommunication networks. p.1114

Figure 35. 30 The construction of an optical fiber Figure 35.30 The construction of an optical fiber. Light travels in the core, which is surrounded by a cladding and a protective jacket. Fig 35-30, p.1114

Figure 35.29 Light travels in a curved transparent rod by multiple internal reflections. Fig 35-29, p.1114