▁to ▁the ▁sources ▁on ▁the ▁far ▁side ▁of ▁the ▁volume ▁fast ▁enough . ▁As ▁a ▁result , ▁perfect ▁clo aking ▁for ▁light ▁is ▁still ▁probably ▁at ▁least ▁very ▁difficult ▁if ▁not ▁impossible . ▁For ▁sound ▁waves , ▁though , ▁such ▁perfect ▁clo aking ▁is ▁possible ▁in ▁principle ; ▁an ▁object ▁could ▁therefore ▁be ▁made ▁invisible ▁to ▁son ar , ▁for ▁example . ▁ ▁According ▁to ▁F erm at ’ s ▁Princi ple , ▁light ▁follows ▁the ▁traject ory ▁of ▁the ▁short est ▁optical ▁path , ▁that ▁is , ▁the ▁path ▁over ▁which ▁the ▁integral ▁of ▁the ▁ref ract ive ▁index ▁function ▁is ▁minimal . ▁Therefore , ▁the ▁ref ract ive ▁index ▁of ▁an ▁optical ▁medium ▁determ ines ▁how ▁light ▁propag ates ▁within ▁it . ▁Con sequently , ▁by ▁a ▁suitable ▁choice ▁of ▁ref ract ive ▁index ▁profile ▁for ▁an ▁optical ▁medium , ▁light ▁ray s ▁can ▁be ▁bent ▁around ▁and ▁made ▁to ▁propag ate ▁in ▁closed ▁loops . ▁ ▁See ▁also ▁ ▁Ac oust ic ▁clo ak ▁ ▁Clo aking ▁device ▁ ▁Magic ▁ring ▁ ▁Nach t ▁und ▁Neb el ▁ ▁References ▁ ▁Bibli ography ▁ ▁Further ▁reading ▁Clo aking ▁and ▁In visibility : ▁Fact ▁and ▁F iction ▁by ▁Professor ▁David ▁R . ▁Smith ▁- ▁Elect rical ▁and ▁Computer ▁Engineering ▁- ▁Duke ▁University ▁( May ▁ 2 8 , ▁ 2 0 0 6 ) ▁Three - dimensional ▁optical ▁met am aterial ▁with ▁a ▁negative ▁ref ract ive ▁index ▁by ▁Jason ▁Valent ine , ▁Sh u ang ▁Z hang , ▁Thomas ▁Zent g