# Chapter 17: Wave Optics. What is Light? The Models of Light 1/11/13

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1 Chapter 17: Wave Optics Key Terms Wave model Ray model Diffraction Refraction Fringe spacing Diffraction grating Thin-film interference What is Light? Light is the chameleon of the physical world. Under some circumstances, light acts like particles traveling in straight lines. Under other circumstances, light shows the same wave-like behavior as sound waves or water waves. The Models of Light Wave Model light acts like any other wave Most useful for: lasers, electro-optical devices Ray Model light travels in straight-line paths Most useful for: prisms, mirrors, lenses Photon Model light is both wave and particle Most useful for: quantum studies 1

2 Diffraction The spreading of a wave to fill the space behind or around an opening or obstacle. 2

3 Diffraction and Wavelength Whether a wave spreads out or travels straight ahead is dependent upon the size of the obstacle and the size of the wave. Light has extremely short wavelengths ( nm), so an extremely small obstacle is required to cause diffraction. Index of Refraction Light waves travel with a speed c =3.00 x 10 8 m/s in a vacuum, but they slow down as they pass through other transparent materials. The speed of light in a material is characterized by the material s index of refraction. Sample Problem #1 (ex. 17.1, page 548) Orange light with a wavelength of 600 nm is incident on a 1.00 mm thick glass microscope slide. What is the light speed in the glass? How many wavelengths of the light are in the glass? 3

4 The Interference of Light Young s Double-Slit Experiment Light spreads out between each slit (diffraction), and the two spreading waves overlap in the region between the slits and a screen (interference). Sample Problem #2 (ex. 17.2, page 551) Light from a helium-neon laser (λ= 633 nm) illuminates two slits spaced 0.40 mm apart. A viewing screen is 2.0 m behind the slits. A bright fringe is observed at a point 9.5 mm from the center of the screen. What is the fringe number? 4

5 Sample Problem #3 (ex. 17.3, page 552) A double-slit interference pattern is observed on a screen 1.0 m behind two slits spaced 0.30 mm apart. From the center of one particular fringe to the center of the ninth fringe from this one is 1.6 cm. What is the wavelength of this light? Extra Problem In a Young s double slit experiment, a monochromatic light of wavelength nm is used. The slit separation is 0.4 mm and the slit is placed 1.5 m from the screen. Determine the fringe width. the angular position of the 10 th bright fringe from the center. the linear position of the 10 th bright fringe from the center. The Diffraction Grating A diffraction grating is an opaque screen that has many closely spaced slits. When illuminated from one side, each of these slits becomes the source of a wave that diffracts. 5

6 Extra Problem A diffraction grating has 600 lines/mm. A light of wavelength 480 nm is incident on the grating. Determine the angular positions for the 1 st and 2 nd maxima. Thin-Film Interference The interference of light waves reflected from the two boundaries of a thin film. Ex: the thin film of water that makes a soap bubble. Thin-film coatings are used for the antireflective coatings on the lenses in cameras, microscopes, and other optical equipment. The interference of light reflecting off a thin film depends on the path-length difference and the number of phase changes undergone by the light. A light wave undergoes a phase change if it reflects from a boundary at which the index of refraction increases. A phase change results in an inverted wave. 6

7 Sample Problem #5 (ex. 17.5, page 558) To keep unwanted light from reflecting from the surface of eyeglasses, a thin film of a material with an index of refraction n = 1.38 is coated onto the plastic lens (n = 1.55). It is desired to have destructive interference for λ= 550 nm because that is the center of the visible spectrum. What is the thinnest film that will do this? Sample Problem #6 (P. 570 #22) A very thin oil film (n = 1.25) floats on water (n = 1.33). What is the thinnest film that produces a strong reflection for green light with a wavelength of 500 nm? Single-Slit Diffraction 7

8 Sample Problem #7 (ex. 17.8, page 564) Light from a helium-neon laser (λ= 633 nm) passes through a narrow slit and is seen on a screen 2.0 m behind the slit. The first minimum in the diffraction pattern is 1.2 cm from the middle of the central maximum. How wide is the slit? 8

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