Young's double-slit experiment © 2014 Pearson Education, Inc.

Qualitative wave-based explanation of Young's experiment © 2014 Pearson Education, Inc.

Interference An interference pattern can be explained using the idea of interference of wavelets. Constructive interference occurs when the crests from the wavelets overlap, resulting in double-sized crests. Destructive interference means no light is present: the wavelets are out of phase and cancel each other out. © 2014 Pearson Education, Inc.

Quantitative analysis of the double-slit experiment Waves in phase give constructive interference. Waves completely out of phase give destructive interference. © 2014 Pearson Education, Inc.

Mathematical location of the mth bright band Using trigonometry, we find: © 2014 Pearson Education, Inc.

Mathematical location of the mth bright band We can find the distance between the zero-order maximum and the mth maximum: If the angle is very small, we can approximate and find: © 2014 Pearson Education, Inc.

Double-slit interference © 2014 Pearson Education, Inc.

Tip © 2014 Pearson Education, Inc.

Young's interference with white light When white light is used in the double-slit experiment, we see the following: Because the angular deflection of red light appears greater than that of blue light, we can conclude that red light must have a longer wavelength than blue light. © 2014 Pearson Education, Inc.

Relating the refractive index and the speed of light in a substance The wave model of light not only explains why light bends at the boundary of two media, but also explains Snell's law by connecting the medium's index of refraction to the speed of light in that medium. © 2014 Pearson Education, Inc.

Refractive index © 2014 Pearson Education, Inc.

Does the refractive index depend on the color of the light? The different indexes of refraction for different colors mean that light of different colors and light waves of different frequencies travel at different speeds in the same medium. © 2014 Pearson Education, Inc.

Tip © 2014 Pearson Education, Inc.

Chromatic aberration in lenses: A practical problem in optical instruments The image locations for each wavelength of light are slightly different, leading to distortions: © 2014 Pearson Education, Inc.

Monochromatic and coherent waves We don't observe an interference pattern from two light bulbs. The waves are not coherent; they add together randomly and produce no interference pattern on the wall. © 2014 Pearson Education, Inc.

Monochromatic and coherent waves © 2014 Pearson Education, Inc.

Coherent monochromatic waves © 2014 Pearson Education, Inc.

Gratings: An application of interference A typical grating has hundreds of slits per millimeter. The bright bands are very intense and narrow, with almost complete darkness between them. © 2014 Pearson Education, Inc.

Tip © 2014 Pearson Education, Inc.

White light incident on grating A spectrum produced by a grating is a result of the light of different wavelengths interfering constructively at different locations. © 2014 Pearson Education, Inc.

CDs and DVDs: Reflection gratings The grooves in a CD play the role of the slits: the reflected white light forms interference maxima for different colors at different angles. © 2014 Pearson Education, Inc.

Spectrometer A spectrometer is used to analyze wavelengths of light from different sources. © 2014 Pearson Education, Inc.

Thin-film interference The beautiful, swirling colors on soap bubbles, oil slicks, butterfly wings, and a peacock's tail feathers are the result of thin-film interference. © 2014 Pearson Education, Inc.

Bright and dark bands due to reflected monochromatic light © 2014 Pearson Education, Inc.

Bright and dark bands due to reflected monochromatic light Two factors affect the way in which the light reflected from the front surface combines with the light reflected from the back surface. Phase change upon reflection Phase difference due to path-length difference © 2014 Pearson Education, Inc.

Path-length difference due to refractive index If the refractive index of the thin film is greater than 1.0, then the wavelength of the light in the film is: © 2014 Pearson Education, Inc.

Thin film on glass surface Glass surfaces are often covered with a thin film. Waves reflecting from the film interfere with one another destructively, minimizing reflected light. © 2014 Pearson Education, Inc.

Examples of thin-film interference for monochromatic incident light © 2014 Pearson Education, Inc.

Examples of thin-film interference for monochromatic incident light © 2014 Pearson Education, Inc.

Reflection patterns on a soap bubble in white light Usually white light (wavelengths from 400 to 700 nm) is incident on a thin film. Due to different wavelengths, different thicknesses, and different angles, light of only a small wavelength range is destructively reduced in intensity at any particular location on a soap bubble. © 2014 Pearson Education, Inc.

Complementary colors Complementary colors are the white light colors that are left when light of a small wavelength range is subtracted. Complementary colors are not the same as the spectrum produced by a grating or a prism. These devices separate in space the primary colors that are combined spatially inside a beam of white light. © 2014 Pearson Education, Inc.

Tip © 2014 Pearson Education, Inc.

Lens coatings We can reduce the reflected light of a particular wavelength if we have a film of a particular thickness. The thickness of the coating on glass lenses for cameras, microscopes, and eyeglasses is usually chosen to reduce light at a wavelength of 550 nm, the center of the visible spectrum. A lens with a thin-film coating has a purple hue because it reflects red and violet light more than other colors. © 2014 Pearson Education, Inc.

Bird and butterfly colors Many colors in the natural world, such as those of flower petals and leaves, are caused by organic pigments that absorb certain colors and reflect others. Some feathers and insect bodies consist of microscopic translucent structures that act like thin films to produce destructive and constructive interference of light. © 2014 Pearson Education, Inc.

Tip © 2014 Pearson Education, Inc.

Diffraction of light If you look carefully at the pattern produced by light passing through two slits on the screen, you will notice that in addition to the alternating bright and dark bands, there is an overall periodic modulation of the brightness in the pattern. © 2014 Pearson Education, Inc.

Quantitative analysis of single-slit diffraction The width of the central diffraction maximum (the central bright band on the screen) increases as the width of the slit decreases. © 2014 Pearson Education, Inc.

Quantitative analysis of single-slit diffraction In the single-slit situation, the slit is not infinitely narrow. © 2014 Pearson Education, Inc.

Tip © 2014 Pearson Education, Inc.

Single-slit diffraction © 2014 Pearson Education, Inc.

The Poisson spot: A historical testing of the wave model of light © 2014 Pearson Education, Inc.

Resolving power: Putting it all together © 2014 Pearson Education, Inc.

Resolving ability of a lens © 2014 Pearson Education, Inc.

Rayleigh criterion © 2014 Pearson Education, Inc.

Tip © 2014 Pearson Education, Inc.

Skills for analyzing processes using the wave model of light When problem solving: Decide if the sources in the problem produce coherent waves. Decide if the small-angle approximation is valid. Decide if the slit widths for multiple slits are wide enough that you have to consider single-slit diffraction as well as multiple-slit interference. If useful, represent the situation with a wave front diagram showing the overlapping crests and troughs of the light waves from different sources. © 2014 Pearson Education, Inc.

Summary © 2014 Pearson Education, Inc.

Summary © 2014 Pearson Education, Inc.

Summary © 2014 Pearson Education, Inc.

Summary © 2014 Pearson Education, Inc.

Summary © 2014 Pearson Education, Inc.

Summary © 2014 Pearson Education, Inc.

Summary © 2014 Pearson Education, Inc.

Summary © 2014 Pearson Education, Inc.