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EM Spectrum Physics 102 Professor Lee Carkner Lecture 27

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PAL #26 EM Waves Changing C of LC oscillator f and C have an inverse square root relationship Increase the frequency Decrease the frequency Double the frequency Tune in WVIK (90.3 MHz) with L = 1X10 -8 H (LC) ½ = 1/2 f C = [1/(2)( )(90.3X10 6 )] 2 (1/1X10 -8 ) = 3.1X10 -10 F

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Energy in EM Wave Each has an energy density: u E = u B = The total energy density is the sum of each term This energy density is not very useful Called the intensity, I

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Intensity of Flashlight

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Intensity Use E rms or B rms to get average The energy density of each field is the same The intensity depends on how much energy the wave delivers, which depends on the energy density and the speed: I = I = c 0 E rms 2 Units: joules per second per square meter (W/m 2 )

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Intensity of Light We normally don’t know much about the E field of a light wave, but rather we know something about the source of the wave As the waves travel out the power is spread out over a sphere of radius r (r is the distance away): I = P s / 4 r 2 Light (like sound) falls off with an inverse square law

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Inverse Square Law

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Radiation Pressure If someone shines a flashlight on you, the light is trying to push you away EM pressure is due to the fact that light has momentum which can be transmitted to an object through absorption or reflection

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Comet Hale- Bopp

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Momentum Transfer The change in momentum due to light is given by: Where p is the momentum change and U is the energy change For reflection the momentum change is twice as much: p = 2 U/c

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Light Pressure From Newton’s second law The amount of energy delivered in time t is: where I is the intensity and A is the area p r = I/c (total absorption) p r = 2I /c (total reflection)

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Solar Sail

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Example: Light Sail Radiation pressure can be used to power a spacecraft The sail can gather light from a star to propel the spacecraft Light sail powered craft need no engines or fuel

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Today’s PAL Consider a light sail craft near the Earth with a mass of 5 tons (5000 kg) and a sail area of 2.25 x 10 8 m2 (about 15 by 15 km). The sail is made from a lightweight, thin, and highly reflective fabric and is powered by sunlight (distance to sun = 1.5 X 10 11 meters, power of sun 3.9 X 10 26 W). a) What is the intensity of sunlight for the spacecraft? b) How much light pressure does the spacecraft feel? c) What is the acceleration of the spacecraft (remember F = ma, p = F/A)?

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The Electromagnetic Spectrum Electromagnetic radiation can have any wavelength This is where our Sun produces the most light, so our eyes have evolved to detect it We will use the terms “light”, “photons” and “electromagnetic (EM) radiation or waves” interchangeably

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EM Waves and Energy The energy of an EM wave is proportional to the frequency where h = Planck’s constant = 6.63 X 10 -34 J s Radio waves and X-rays produce different effects

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The Electromagnetic Spectrum

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The EM Spectrum Radio Low energy but good penetration Millimeter (microwave) Also good for communication Infrared Emitted strongly by living things Visible What your eyes see

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The EM spectrum Ultraviolet High energy X-ray Strongly penetrating Gamma Ray Hard to produce Get from H bombs, etc.

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Atmospheric Transmission Gamma + X-ray blocked Infrared blocked O 2, N 2 Absorption H 2 O, CO 2 Absorption

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Sensitivity of Your Eye

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Light from the Sun The sun (like all stars) is actually producing EM waves with a variety of wavelengths via many different processes The sun’s visible light is thermal (blackbody) radiation The sun produces more yellow and red light than blue, so the sun looks orange

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Solar Emission Spectrum

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Monday’s Sun in Visible Light

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Radio Waves from the Sun

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A Coronal Loop

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Solar Spectrum Sun emits most strongly at visible wavelengths Produces stronger IR at cooler regions Produces high energy radiation in outer layers Also produces low energy radiation in magnetic loops

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Next Time Read 24.10 Homework, Ch 22, P 21, Ch 24, P 53, 57 Final exam: Section 1: Tuesday 9 am Section 2: Thursday 12 noon

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