MOTION MOUNTAIN

350 challenge hints and solutions
b
a
c
β
Ref. 97
Input and output beams are antiparallel,
β determines the polarization rotation.
Input and output beams are parallel,
the length ratios a : b : c determine the
polarization rotation.
F I G U R E 174 Two mirror arrangements that rotate the polarization of a light beam by a predetermined
angle.
Challenge 147, page 138: Three mirrors is the minimum. Two such mirror arrangements are
shown in Figure 174. There is also a three-mirror arrangement with parallel input and output
beams;canyoufindit?Theideasbehindthesearrangementsarewellexplainedinthepapers by
EnriqueGalvez andhiscollaborators.
Challenge 148, page 138: In the left interferometer, light exits in direction B, in the right one,
indirectionA.Theproblemcanalsobegeneralized toarbitrary interferometer shapes.Theway
to solve it in this case is the use of Berry’s phase. If you are interested, explore this interesting
conceptwiththehelpofyourfavourite library.
Challenge 149, page 143: The average temperature of the Earth is thus287 K. The energy from
the Sun is proportionalto the fourth power of the temperature. The energy is spread (roughly)
overhalftheEarth’ssurface.Thesameenergy,attheSun’ssurface,comesfromamuchsmaller
surface,given bythesameangleastheEarth subtendsthere.WethushaveE∼2πR 2 Earth T4 Earth =
T 4 Sun R2 Earth α2 ,whereαishalftheangle subtendedbytheSun.Asaresult, thetemperatureof the
SunisestimatedtobeT Sun =(T 4 Earth /α2 ) 0.25 =4 kK.
Challenge 153, page 144: Because themaximumof a spectruminwavelengths andin frequenciesisnotthesame,thusdoesnot
andcannotfollowc=fλ.
Challenge 156, page 145: At high temperature, all bodies approach black bodies. The colour is
moreimportantthanothercoloureffects. Theoven andtheobjectshavethesametemperature.
Thus they cannot bedistinguishedfrom each other. Todo so nevertheless, illuminate the scene
withpowerful lightand thentake apicturewith small sensitivity.Thusonealwaysneeds bright
lighttotakepicturesofwhathappensinsidefires.
Challenge 157, page 146: Achievingahighertemperaturewouldallowtobreakthesecondprincipleofthermodynamics.Toexplorethisquestionfurther,readintextbooksabouttheso-called
Kirchhofflaws.
Challenge 158, page 147: Theeffectivetemperatureoflaserlightcanalsobedescribedashigher
thaninfinite;thisallowsalsotoheattargets toextremely hightemperatures.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net