Models of Light

1. Models of Light • The wave model: under many circumstances, light exhibits the same behavior as sound or water waves. The study of light as a wave is called wave optics. • The ray model: The properties of prisms, mirrors, and lenses are best understood in terms of light rays. The ray model is the basis of ray optics. • The photon model: In the quantum world, light behaves like neither a wave nor a particle. Instead, light consists of photons that have both wave-like and particle-like properties. This is the quantum theory of light.

2. The Nature of Light • When studying geometric optics, we used a ray model to describe the behavior of light. • A wave model of light is necessary to describe phenomena such as: • interference • diffraction • A particle model of light is necessary to describe phenomena observed in modern physics, for example, the interaction between light and atoms. We’ll get back to this later... Light as a Wave

3. Wave Nature of Light • Christian Huygens (1629-1695) • contemporary of Newton • developed wave theory of light • Huygen’s Principle • Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave itself. • The new wave front is the envelope of all the wavelets - tangent to all of them Light as a Wave

4. Huygen’s Principle Light as a Wave

5. Diffraction • Huygen’s Principle is useful for understanding diffraction - the bending of waves behind obstacles into the shadow region Light as a Wave

6. Interference • Thomas Young (1773-1829) • definitively (at least temporarily) demonstrates wave nature of light • Young’s Double-Slit Experiment • coherent light passes through 2 slits, S1 and S2 • light from S1 and S2 then interferes and pattern of dark and light spots is observed on the screen Light as a Wave

7. Interference • Constructive interference occurs when • d sin = m  , m = 0,1,2,... • m = order • Destructive interference occurs when • d sin = (m + 1/2)  , m = 0,1,2,... • Source must be coherent • waves at S1 and S2 are in-phase Light as a Wave

8. what you see on the screen Light as a Wave

9. Think-Pair-Share • Monochromatic light falling on two slits 0.016 mm apart produces the fifth-order fringe at an 8.8 degree angle. What is the wavelength of the light used? Light as a Wave

10. Conceptual Question • What happens to the interference pattern if the wavelength of light is increased from 500 nm to 700 nm? • What happens instead if the wavelength stays at 500 nm but the slits are moved farther apart? Light as a Wave

11. Pair Problem • Light of wavelength 680 nm falls on two slits and produces an interference pattern in which the fourth-order fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the separation of the two slits?(Hint: tan =  for small angles, and angles must be in radians!) Light as a Wave

12. Visible Spectrum Light as a Wave

13. Dispersion (L) • Index of refraction varies with wavelength of light • As a result, white light is separated into component colors by a prism or by water (rainbow) Light as a Wave

14. Dispersion & Rainbow (L) • red is bent the least • red light reaches observer’s eye from higher water droplets • violet is bent the most • violet light reaches observer’s eye from lower water droplets Light as a Wave

15. Diffraction by a Disk • Diffracted light interferes constructively at center of shadow • requires a point source of monochromatic light (e.g. laser) Light as a Wave

16. Circular-Aperture Diffraction Light of wavelength λ passes through a circular aperture of diameter D, and is then incident on a viewing screen a distance L behind the aperture, L>>D. The diffraction pattern has a circular central maximum, surrounded by a series of secondary bright fringes shaped like rings. The angle of the first minimum in the intensity is The width of the central maximum on the screen is

18. Diffraction by a Single Slit • D sin  = m  • m = 1, 2, 3, ... position of minima for m=1, theta gives 1/2 width of central maximum Motivation for making large diameter telescopes Light as a Wave

19. Diffraction Grating • a large number of equally spaced parallel slits • same relation as double-slit • d sin  = m  • m = 0, 1, 2, ... • produces sharper and narrower interference patterns that double slit Light as a Wave

20. Diffraction Grating • double slit versus diffraction grating • for multi-wavelength light Light as a Wave

21. Emission Tubes • Look at several emission tubes using diffraction gratings & sketch spectrum • Foundation of spectroscopy, a technique used in numerous scientific applications Element Light as a Wave

22. Measuring Indices of Refraction A Michelson interferometer can be used to measure indices of refraction of gases. A cell of thickness d is inserted into one arm of the cell. When the cell contains a vacuum, the number of wavelengths inside the cell is When the cell is filled with a specific gas, the number of wavelengths spanning the distance d is Filling the cell has increased the lower path by wavelengths. By counting fringe shifts as the cell is filled, one can determine n.

24. EXAMPLE 22.9 Measuring the index of refraction QUESTION:

25. EXAMPLE 22.9 Measuring the index of refraction

26. EXAMPLE 22.9 Measuring the index of refraction

27. EXAMPLE 22.9 Measuring the index of refraction