Chapter 35

The Nature of Light and the Laws of Geometric Optics (Cont.) PHY 1371 Dr. Jie Zou 1

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 PHY 1371 Dr. Jie Zou 2

Huygens’s Principle

(a) a plane wave traveling to the right (b) a spherical wave traveling to the right PHY 1371  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.

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Huygens’s principle applied to reflection and refraction

Reflection Refraction PHY 1371 Dr. Jie Zou 4

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

PHY 1371   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. Dr. Jie Zou 6

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.

PHY 1371 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 is some particular angle of incidence when the refracted light ray moves parallel to the boundary so that the angle of refraction,  2 = 90°.

 c  For angles of incidence >  c , the beam is  total reflection.

Find

(for n  1

c

from Snell’s law: sin > n 2 ) Dr. Jie Zou  c = n 2 /n 1 9 PHY 1371

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.) Dr. Jie Zou 11 PHY 1371

Homework

 Ch. 35, P. 1120, Problems: #30, 36, 38. PHY 1371 Dr. Jie Zou 12