Wave Nature of Light & Electromagnetic Waves History, Light is a Wave & Polarization History, Light is a Wave & Polarization

Terms Superposition: Algebraic sum of the displacements of waves. Superposition: Algebraic sum of the displacements of waves. Interference: Pattern produced by interfering waves, can be constructive or destructive. Interference: Pattern produced by interfering waves, can be constructive or destructive. Diffraction: The spreading of light beyond a barrier. (Huygens principle applies) Diffraction: The spreading of light beyond a barrier. (Huygens principle applies)

Conditions of Interference Best if monochromatic – single frequency, one color light Best if monochromatic – single frequency, one color light Coherent – Constant phase relationship. Same frequency and in phase. (variance of one’s phase to the other is constant) Coherent – Constant phase relationship. Same frequency and in phase. (variance of one’s phase to the other is constant) Zero Phase difference “In Phase” – Constructive Zero Phase difference “In Phase” – Constructive 180˚ difference in phase – out of phase by ½ λ so it is destructive 180˚ difference in phase – out of phase by ½ λ so it is destructive

Rainbows Chromatic Dispersion Chromatic Dispersion Index of refraction is greater for a shorter wavelength (blue) than for a longer wavelength (red) Index of refraction is greater for a shorter wavelength (blue) than for a longer wavelength (red) Occurs with prisms where white light is spread into its constituant colors. Occurs with prisms where white light is spread into its constituant colors.

Christian Huygens 1678 Every point of a wave front may be considered the source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the waves. Every point of a wave front may be considered the source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the waves.

Thomas Young, 1801 Experiment demonstrated the wave nature of light and Experiment demonstrated the wave nature of light and Allows one to determine the wavelength, λ of a beam of light Allows one to determine the wavelength, λ of a beam of light Measured the average wavelength of sunlight. (570 nm measured – Current is 550 nm. Very close!) Measured the average wavelength of sunlight. (570 nm measured – Current is 550 nm. Very close!)

Newton was wrong If light had been particles or corpuscles as Newton considered them, then it would pass directly through the slits to the screen beyond in Young’s experiment. If light had been particles or corpuscles as Newton considered them, then it would pass directly through the slits to the screen beyond in Young’s experiment. This did not happen! This did not happen!

Phase difference can change… The phase difference between two waves can change if the waves travel paths of different lengths. The phase difference between two waves can change if the waves travel paths of different lengths.

Path Length Differences Equal to mλ - constructive & bright fringe Equal to mλ - constructive & bright fringe Equal to ½mλ - destructive and dark fringe. Equal to ½mλ - destructive and dark fringe.

Interference from path difference If d << L then the difference in path length travelled by the two rays is approximately: r1 - r2 ≈ dsin θ If d << L then the difference in path length travelled by the two rays is approximately: r1 - r2 ≈ dsin θ Where θ is approximately equal to the angle that the rays make relative to a perpendicular line joining the slits to the screen. Where θ is approximately equal to the angle that the rays make relative to a perpendicular line joining the slits to the screen.

Bright & Dark Fringes If the rays were in phase when they passed through the slits, then the condition for constructive interference at the screen is: dsinθ = m λ, m = ±1, ±2,... If the rays were in phase when they passed through the slits, then the condition for constructive interference at the screen is: dsinθ = m λ, m = ±1, ±2,... The condition for destructive interference at the screen: dsinθ= (m + ½)λ, m = ±1, ±2,... The condition for destructive interference at the screen: dsinθ= (m + ½)λ, m = ±1, ±2,... Where m is the order of the interference fringe. (m=1 is on either side of the central fringe) Where m is the order of the interference fringe. (m=1 is on either side of the central fringe)

When y << L sin θ ≈ y/L (Your text uses x instead of y) sin θ ≈ y/L (Your text uses x instead of y) So y = λmL/d So y = λmL/d

Diffraction Grating Large number of equally spaced parallel slits. Large number of equally spaced parallel slits. Creates even sharper and narrower bright maxima than Young’s Double Slit. Creates even sharper and narrower bright maxima than Young’s Double Slit. Useful for precise measurements of wavelengths. Useful for precise measurements of wavelengths.

Thin Film Interference Interference of light waves reflecting off the top surface of a film with the waves reflecting from the bottom surface Interference of light waves reflecting off the top surface of a film with the waves reflecting from the bottom surface

Examples of Thin Film Interference CD CD Oil Oil Soap Bubble Soap Bubble

Electromagnetism

James Clerk Maxwell 1864 Hypothesized that since a changing magnetic field produces an electric field (Faraday’s Law) the opposite could be true. Hypothesized that since a changing magnetic field produces an electric field (Faraday’s Law) the opposite could be true. Worked out mathematically these described: Worked out mathematically these described: Charge Density and the Electric Field Charge Density and the Electric Field The Structure of the Magnetic Field The Structure of the Magnetic Field A Changing Magnetic Field and the Electric Field A Changing Magnetic Field and the Electric Field The Source of the Magnetic Field The Source of the Magnetic Field

Leading to… Electric and magnetic fields acting together could produce an electromagnetic wave which travels at the speed of light. Electric and magnetic fields acting together could produce an electromagnetic wave which travels at the speed of light. Prior to this, visible light was thought of as a completely separate phenomenon. Prior to this, visible light was thought of as a completely separate phenomenon. Now light is understood to be an electromagnetic wave Now light is understood to be an electromagnetic wave His theory also implied that electromagnetic waves were not limited to visible light. His theory also implied that electromagnetic waves were not limited to visible light.

Heinrich Hertz, 1887 First produced and observed EM waves in a laboratory setting using LC circuit. First produced and observed EM waves in a laboratory setting using LC circuit. Observed energy transfer Observed energy transfer Observed normal wave behavior such as reflection, refraction, interference, diffraction and polarization. Observed normal wave behavior such as reflection, refraction, interference, diffraction and polarization.

Hertz’s Experiment Showed Wave was produced in one circuit and propagated across the room to a second circuit. Wave was produced in one circuit and propagated across the room to a second circuit. The wave moved at the speed of light! The wave moved at the speed of light!

Leading us to Marconi Guglielmo Marconi 1896 recognized the implications of the EM wave experiments. Guglielmo Marconi 1896 recognized the implications of the EM wave experiments. Waves could be used for communications, eliminating the need for telegraph wires. Waves could be used for communications, eliminating the need for telegraph wires. Radio Signal Radio Signal Sent from Cornwall England Sent from Cornwall England Received in St. Johns Newfoundland Received in St. Johns Newfoundland

How does a turtle find a new pond? Polarization Polarization In general: The polarization of an EM wave refers to the direction of its electric field. In general: The polarization of an EM wave refers to the direction of its electric field. Light from the sun or an incandescent bulb is unpolarized. Light from the sun or an incandescent bulb is unpolarized.

How is light polarized… Pass a beam of light through a polarizer. Pass a beam of light through a polarizer. Polarizer is a material that is composed of long thin electrically conductive molecules oriented in a specific direction. Polarizer is a material that is composed of long thin electrically conductive molecules oriented in a specific direction. Reflected light is polarized Reflected light is polarized

Polarizer When unpolarized light hits a single layer of polarizing material ½ the light goes through. When unpolarized light hits a single layer of polarizing material ½ the light goes through. If a second sheet is at a right angle to the first, no light will transmit through the second sheet. If a second sheet is at a right angle to the first, no light will transmit through the second sheet.

Sources magnets.com/magnet_university/maxwells_equations.htm magnets.com/magnet_university/maxwells_equations.htm magnets.com/magnet_university/maxwells_equations.htm magnets.com/magnet_university/maxwells_equations.htm Physics, 4 th Edition, Walker, James S.; Pearson Education, Physics, 4 th Edition, Walker, James S.; Pearson Education, vafigure1.jpg vafigure1.jpg vafigure1.jpg vafigure1.jpg electron9.phys.utk.edu electron9.phys.utk.edu _bca0ca1618.jpg&imgrefurl= or/ /&usg=__ie2UMG4sRMWzwWSe7ac08SVc3wk=&h=323&w=50 0&sz=134&hl=en&start=14&sig2=Qx_gTEINw9DL7yIaLbVzBg&um=1&tbni d=76kvXn- pi9o1hM:&tbnh=84&tbnw=130&prev=/images%3Fq%3DThin%2BFilm%2B interference%26hl%3Den%26sa%3DN%26um%3D1&ei=J3nZSfX- IN3elQeT16jQDA _bca0ca1618.jpg&imgrefurl= or/ /&usg=__ie2UMG4sRMWzwWSe7ac08SVc3wk=&h=323&w=50 0&sz=134&hl=en&start=14&sig2=Qx_gTEINw9DL7yIaLbVzBg&um=1&tbni d=76kvXn- pi9o1hM:&tbnh=84&tbnw=130&prev=/images%3Fq%3DThin%2BFilm%2B interference%26hl%3Den%26sa%3DN%26um%3D1&ei=J3nZSfX- IN3elQeT16jQDA