MOTION MOUNTAIN

challenge hints and solutions 353
sity Press, 1993, or explore dedicated websites, such as www.mikroskopie-muenchen.de or micro.
magnet.fsu.edu/primer/techniques.
Challenge 169, page 159: Thedispersionatthelensleadstodifferentapparentimagepositions,
asshowninFigure176.Formoredetailsonthedispersioninthehumaneyeandthewaysofusing
ittocreatethree-dimensionaleffects,seethearticlebyC. Ucke&R. Wolf,DurchFarbeindie
dritteDimension, PhysikinunsererZeit30,pp.50–53,1999.
Challenge 170, page 162: The1 mm beam would return 1000times aswideas the1 m beam. A
perfect1 m-wide beam of green light would be209 m wide on the Moon; can you deduce this
resultfromthe(important)formulathatinvolvesdistance,wavelength,initialdiameterandfinal
diameter?Trytoguessthisbeautifulformula first,andthendeduceit.Inreality,thevalues area
fewtimeslargerthanthetheoreticalminimumthuscalculated.Seethewww.csr.utexas.edu/mlrs
andilrs.gsfc.nasa.gov websites.
Challenge 171, page 162: Itisoften saidthatevolutiontuned thenumberofconesintheeyeto
themaximumresolutionwithopenpupil;theexpertsonthesubjecthowevermaintainthatthere
aresomewhatlarger numbersofcones.
Challenge 172, page 162: Theanswershouldliebetweenoneortwodozenkilometres,assuming
idealatmosphericcircumstances.
Challenge 175, page 171: In fact, there isno way that a hologramof a personcan walk around
andfrightenarealperson.Ahologramisalwaystransparent;onecanalwaysseethebackground
throughthehologram.Ahologramthusalwaysgivesanimpressionsimilartowhatmovingpicturesusually
showasghosts.Ifthebackgroundisblack,shinewithatorchontoittofindout.
Challenge 176, page 172: Thesmallwavelengthoflightprobablypreventsachievingthisdream.
Foratrueholographicdisplay,thepixelsneedtobesmallerthanthewavelengthoflightandmust
beableto reproduce phaseinformation.Thus thenext questionis:howmuch ofthedream can
berealized? Ifyoufindasolution,youwillbecomerichandfamous.
Challenge 178, page 178: There is a blind spot in the eye; that is a region in which images are
notperceived.Thebrainthanassumesthattheimageatthatplaceisthesamethanatitsborders.
Ifaspotfalls exactly insideit,itdisappears.
Challenge 179, page 178: The mechanism that compensates the missing blue receptors in the
fovea doesnotworksorapidly:youwillseeaspotduetothefovea.
Challenge 181, page 179: Theeyeandbrainsurelydonotswitchtheupandthedowndirection
atacertainage.Besides,wheredoestheideacomefromthatbabiesseeupside-down?
Challenge 182, page 187: Theeyeandvisionsystemsubtractpatternsthatareconstantintime.
Challenge 183, page 188: Not really; a Cat’s-eye uses two reflections at the sides of a cube. A
livingcat’seyehasalargenumberofreflections.Theendeffectisthesamethough:lightreturns
backtothedirectionitcamefrom.
Challenge 185, page 194: Use diffraction; watch the pattern on a wall a few metres behind the
hair.
Challenge 187, page 195: At10 pc=32.6 al, the Sun would have apparent magnitude 4.7. At
20 pc=65.2 al, it would appear 4 times fainter, thus about 1.5 magnitudes more, therefore with
an apparent visual magnitude of about 6.2. This is near the limit magnitude of the eye. The actual
limiting magnitude of the eye is neither constant nor universal, so the distance of 50 light
years is not a sharp limit. The limiting magnitude, – like the night vision, or scotopic sensitvity
–dependsonthepartialpressureofoxygen intheatmospheretheobserverisbreathing,onthe
clarityoftheair,onthezenithdistance,and,aboveall,onthedegree ofdarkadaptation.Aneye
exposed tothefull brightnessofthenightskyinavery dark locationfar fromlightpollutionis
still not completely dark-adapted. You can easily see 7th-magnitude stars by blocking off most
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net