PHY 1371Dr. Jie Zou1 Chapter 35 The Nature of Light and the Laws of Geometric Optics (Cont.)

PHY 1371Dr. Jie Zou2 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 1371Dr. Jie Zou3 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

PHY 1371Dr. Jie Zou4 Huygens’s principle applied to reflection and refraction ReflectionRefraction

PHY 1371Dr. Jie Zou5 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.

PHY 1371Dr. Jie Zou6 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.

PHY 1371Dr. Jie Zou7 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.

PHY 1371Dr. Jie Zou8 Formation of a rainbow Refraction of sunlight by a spherical raindrop. The formation of a rainbow.

PHY 1371Dr. Jie Zou9 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 = n 2 /n 1 (for n 1 > n 2 )

PHY 1371Dr. Jie Zou10 Fiber optics Light travels in a curved transparent rod by multiple internal reflections.

PHY 1371Dr. Jie Zou11 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.)

PHY 1371Dr. Jie Zou12 Homework Ch. 35, P. 1120, Problems: #30, 36, 38.