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Chapter 35

The Nature of Light and the Laws of Geometric Optics

(Cont.)

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Outline Huygens’s principle

Revisit the laws of reflection and refraction using Huygens’s principle

Dispersion and prisms Prism spectrometer Formation of a rainbow

Total internal reflection An application: Fiber optics

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Huygens’s Principle Huygens’s principle: All

points on a given wave front are taken as point sources for the production of spherical secondary waves, called wavelets, which propagate outward through a medium with speeds characteristic of waves in that medium. After some time has elapsed, the new position of the wave front is the surface tangent to the wavelets.(a) a plane wave traveling to the

right

(b) a spherical wave traveling to the right

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Huygens’s principle applied to reflection and refraction

Reflection

Refraction

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Dispersion Dispersion: The index of

refraction n varies with the wavelength of the light passing through a given material. This behavior is called dispersion.

The index of refraction generally decreases with increasing wavelength.

Blue light bends more than red light does when passing into a refracting material.

Light of different wavelengths is bent at different angles when incident on a refracting material.

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Prism Angle of deviation: A ray of single-

wavelength light incident on the prism from the left emerges refracted from its original direction of travel by an angle , called the angle of deviation.

When a beam of while light (a combination of all visible wavelengths) is incident on a prism, the rays that emerge spread out in a series of colors known as the visible spectrum.

In order of decreasing wavelength: red, orange, yellow, green, blue, and violet.

The angle of deviation depends on wavelength.

Violet light deviates the most and the red light the least.

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Prism spectrometer Prism spectrometer:

An instrument commonly used to study the wavelengths emitted by a light source.

All hot, low-pressure gases emit their own characteristic spectra. The particular wavelengths emitted by a gas serve as “fingerprints” of that gas.

A prism spectrometer can be used to identify gases.

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Formation of a rainbow

Refraction of sunlight by a spherical raindrop.

The formation of a rainbow.

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Total internal reflection Total reflection occurs only when

light moves from a medium of a given index of refraction to a medium of lower index of refraction.

Critical angle c: The critical angle c is some particular angle of incidence when the refracted light ray moves parallel to the boundary so that the angle of refraction, 2 = 90°.

For angles of incidence > c, the beam is entirely reflected at the boundary, hence total reflection.

Find c from Snell’s law: sin c = n2/n1 (for n1 > n2)

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Fiber optics

Light travels in a curved transparent rod by multiple internal reflections.

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Example: Problem #38 Find the maximum angle

for which the light rays incident on the end of the pipe shown in the figure are subject to total internal reflection along the walls of the pipe. (Assume that the pipe has an index of refraction of 1.36 and the outside medium is air.)

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Homework

Ch. 35, P. 1120, Problems: #30, 36, 38.