1Lecture 2 – Chapter 1 •How vision works•What is light•Wavelength and Frequency: c = f λScientific notation and metric unitsElectromagnetic spectrum •Speed of light •Amplitude•DirectionRays and wavefronts•Polarization •Phase differenceWe are hereHomework due next week; see course websiteGo to physics.colorado.edu, and select:-> programs of study -> undergraduate -> physics courses-> Course Home Pages -> Phys 1230 (web page)Ch. 1: How vision worksLight from a source travels to the eye, ORLight from a source is reflected or scattered toward the eye. The sun is self-luminous. The moon shines by scatteredlight.Reflectionin a mirror is a kind of scattering with a special direction (more later).Surface scattering: how we see pages of a book. Light leaves in all directions.Volume scattering:how we see fog, clouds, blue sky.Transparent: no scattering.2What is light?Light is an electromagnetic wave.(uhh...what is electromagnetic? what is a wave?)λ is the wavelength or distance between crests. side view end viewBlue arrow is electric field direction and amplitude, red arrow is magnetic field direction and amplitude. Electric fields make charges “q” move, creating a current. The current can be in your optic nerve, or a solar cell. What is “electromagnetic”?The electromagnetic force is one of 4 fundamental forces.The electromagnetic force includes:• the electric force• the magnetic forceThe unification of the theories of the electric and magnetic forces into a single (beautiful and elegant) theory of electromagnetism is one ofthe great triumphs of physics.The unification of different theories results in overall simplification and increased understanding.3The fundamental forces (interactions)1. gravitational2. electromagnetic3. weak4. strongcelestialterrestrialelectricmagneticelectroweakGUT(GrandUnified Theory)Theory of EverythingIn the future?The unification of terrestrial and celestial gravity(thanks to Isaac Newton)The force that keeps the moon orbiting the earth is the same as the force that makes bricks fall to the floor.This is not at all obvious, though it is now very familiar.People used to think that the moon was pushed (e.g., by angels) around the earth. Newton realized that the moon doesn’t need to be pushed forward around the earth; it tends naturally to move forward. To stay in orbit, the moon needs to be pulled toward the earth. Conclusion: the moon and bricks are both pulled toward the earth by gravitational attraction.4The unification of electric and magnetic forces(thanks to James Maxwell, with help)Fe= kq1q2d2Fm= hI1I2dlThe electric force: a charge produces an electric field which acts upon another chargeThe magnetic force: a current (moving charge) creates a magnetic field which acts upon other moving chargesq1q2dforce of charge q1on charge q2:constant that reflects how strong the electric force isforce of wire 1 carrying current I1on wire 2 carrying current I2:dI1I2constant that reflects how strong the magnetic force is(Notice symmetry between 1 and 2? Newton’s 3rd Law.)lKey insight leading to electromagnetic unification(thanks to Michael Faraday)Faraday showed: a changing magnetic field can create an electric field.(aside: this is how electric generators work--they move a magnet near a wire; moving the magnetic varies the magnetic field, creating an electric field, which moves electrons in the wire).Have you noticed symmetry in physics? For example, the force of object A on object B equals the force of object B on object A (Newton’s 3rd Law).Maxwell suggested that perhaps a changing electric field could create a magnetic field. And he was right....5A traveling electromagnetic disturbanceAssuming Maxwell was right, an amazing thing can happen:if you can somehow produce a varying electric field,then that will create a varying magnetic field, which will continue to create a varying electric field, which will continue to create a varying magnetic field,etc.Moreover, the fields will move in space as they continue to “bootstrap” one another. By measuring the strengths of the electric and magnetic forces,Fe= kq1q2d2Fm= hI1I2dlq1q2dconstant that reflects how strong the electric force isdI1I2constant that reflects how strong the magnetic force isMaxwell’s theory predicts the speed of this electromagnetic disturbance:c = 2kh≈ 300,000,000 m/sl“SI” units of measure(the metric system)• Length: meters (m)• Time: seconds (s)• Velocity: meters/second (m/s)• Frequency: cycles per second or Hertz (Hz)Hz has units 1/s (“per second” or “inverse seconds”)Always state the units for your answers!Useful conversion: 1 m/s is about 2 mph.Maxwell’s traveling electromagnetic disturbance has a speed of about 300,000,000 m/s or 600,000,000 mph -- it’s much easier to write 3x108m/s or 6x108mph.6Scientific notation – powers of 100.1 = 10-11 = 10010 = 1011,000 = 1.0 x 1032,100,000 = 2.1 x 1061/(1,000) = 0.001 = 10-3Calculator notation: 2.1 x 106= 2.1E6Scientific notation – prefixesmilli = 10-3micro = 10-6nano = 10-9kilo = 103mega = 106giga = 109Tera = 1012Common usage:wavelength in mm, μm, or nmfrequency in kHz, MHz, GHz, or THz mμnkMGT7Self-test you can do at home Express the following in scientific notation:1. 137 = ?2. 299792458 = ?3. 0.025 = ?Express the following amounts in different units:1. 2.5 m = ? km2. 2450 MHz = ? GHz3. 1.5x1014Hz = ? THz4. 400 nm = ? mm5. 299792458 m/s = ? m/nsTip for surefire units conversion: multiply by 1, cancel units above and below fractionE.g., 1=1000 m1 km=103 MHz1 GHz=L3.0×108 m/s = 3.0×108 ms 3.048 ft1 m⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1 s109 ns⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 9.1×10−1 ft/ns ≈ 1 ft/nsIf you learn to do these quickly, it will save you time later.It doesn’t take much practice to learn to do these quickly and accurately.=1=1What is a wave?A wave is a propagating disturbance;each “disturbance” disturbs something next to it, which disturbs something next to it, and so the disturbance travels;although the things of which the disturbance is made may not travel much themselves, the wave travels, and it can carry (transport) energy and momentum.Water waves, sound waves, and string waves (a violin string) are familiar examples of waves, though one must observe carefully to distinguish important wave behaviors.Heavy traffic can exhibit wave behavior; so can crowds in a stadium. Are there other examples?8The Speed of LightHow fast does light travel?• Galileo tried to measure