MOTION MOUNTAIN

challenge hints and solutions 349
Page 135
Challenge 120, page 118: Theshinesidegetstwicethemomentumtransferastheblackside,and
thusshouldbepushedbackwards.
Challenge 123, page 120: Rotationof lightcan beunderstoodin two ways:rotating the intensitypattern
around thedirection ofpropagation,orrotatingthepolarizationpattern around the
propagation.Botharepossible:aDoveprismrotatesintensity(andpolarization)andahalf-wave
plate just rotates polarization,for a fixed wavelength. Both aspects can also be rotated with the
mirrorarrangements explainedabove.
Challenge 126, page 121: Theinterferencepatternschangewhencoloursarechanged.Rainbows
alsoappearbecausedifferentcoloursareduetodifferent frequencies.
Challenge 129, page 122: Ternary andquaternary rainbowsformabowaroundtheSun.Tosee
them,typically onehastobebehindabuildingortree thatcovers thedirect viewtotheSun.In
2011,therewereonlyahandfulofphotographsofaternaryrainbowandonlyasinglephotograph
ofaquaternary rainbow,world-wide.
Challenge 130, page 122: The full rainbow is round like a circle. You can produce one with a
gardenhose,ifyoukeep thehoseinyourhandwhileyoustandonachair,withyourbacktothe
evening Sun.(Well,onesmall part ismissing;can youimaginewhichpart?)Thecircleisdue to
thesphericalshapeofdroplets.Ifthedropletswereofdifferentshape,andiftheywereallaligned,
therainbowwould haveadifferentshapethanasimplecircle.
Challenge 133, page 129: Take a film of a distant supernova explosion, or better, an optical or
gamma-rayburst,andcheckwhetherithappensatthesametimeforeachcolourseparately.This
hasbeendoneextensively, andnodifferences havebeen detected withinexperimentalerrors.
Challenge 135, page 131: The first part of the forerunner is a feature with the shortestpossible
effectivewavelength; thusitisgiven bytaking thelimitforinfinitefrequency.
Challenge 136, page 132: Thelightispulsed;thusitistheenergy velocity.
Challenge 137, page 132: Inside matter, the energy is transferred to atoms, then back to light,
thentothenextatoms,etc.Thattakes timeandslowsdownthepropagation.
Challenge 139, page 134: For single photons, permeability, permittivity and the wave impedance
are not well-defined. Conformal invariance, dimensionality and topology are not are not
validatthetinyPlanckscales.Nearblackholes,ifquantumeffects aretaken intoaccount,there
isfrictiononmovingbodies.Quantumfieldtheoryshowsthatvacuumcontainsandconsistsof
virtualparticle–antiparticlepairs.Cosmologyshowsthatthevacuumhasnon-zeroenergy content,
and the same is suggested by quantum field theory. General relativity shows that curved
vacuum can move, and so does quantum gravity. In summary, one can say that vacuum has all
thepropertiesthatwereonceascribedtotheaether,butinawaythatdiffersfundamentallyfrom
whatwasdiscussedbyitsproponents.
Challenge 140, page 134: Almostnolightpasses;theintensityofthelittlelightthatistransmitteddependsexponentiallyontheratiobetweenwavelengthandholediameter.Onealsosaysthat
aftertheholethereisanevanescentwave.
Challenge 141, page 134: The energy density is1 kW/m 2 /c=3.3µJ/m 3 . Assuming sinusoidal
waves, the (root mean square) electric field is√3.3µJ/m 3 /ε 0 =610 V/m – quite a high value.
The(rootmeansquare)magneticfield is610 V/m/c=2.1µT–aratherlowvalue.
Challenge 142, page 134: Anyexampleoflighthasonlyonecolour.
Challenge 144, page 134: Describing light as a substance helps in understanding light beams.
Ontheotherhand,lightisquite aspecial substance:ithasnoeveryday permanence – it can be
absorbed–andithasnomass.
Challenge 145, page 135: Toomuchlightiswasted,thewindshieldsaretooexpensive,andthere
isnoreasontodosomethingifnobodyelsedoes.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net