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Physics 2080; Chapter 28 and 29 Notes

by: Amanda Biddlecome

Physics 2080; Chapter 28 and 29 Notes Physics 2080

Marketplace > Clemson University > Physics 2 > Physics 2080 > Physics 2080 Chapter 28 and 29 Notes
Amanda Biddlecome
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About this Document

These notes cover all of chapter 28 and the beginning of chapter 29.
General Physics 2
Dr. Pope
Class Notes
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This 6 page Class Notes was uploaded by Amanda Biddlecome on Thursday April 7, 2016. The Class Notes belongs to Physics 2080 at Clemson University taught by Dr. Pope in Fall 2016. Since its upload, it has received 16 views. For similar materials see General Physics 2 in Physics 2 at Clemson University.


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Date Created: 04/07/16
Physics  2080   Chapter  28:  Interference  and  Diffraction   April  5,  2016   Amanda  Biddlecome     1)  Superposition  and  Interference     -­‐constructive  or  destructive     -­‐light  can  be  described  using  wave  particles     -­‐constructive=bright  fringes     -­‐destructive=dark  fringes     2)  Young’s  Experiment     -­‐light   goes   through   double   slit   and   have   constructive   and   destructive     interference  (slits  are  very  small)       *get  light  and  dark  fringes       *distance  to  the  screen  is  large  and  distance  between  slits  is  small       *have  a  central  maximum  where  the  light  is  the  brightest       *brightness  diminishes  as  you  get  farther  from  the  central  light     y=Ltanθ   *y=distance  between  peaks  (between  central  and  bright  fringe  that  you’re  looking   at)   *θ=between  central  and  the  bright  fringe     dsinθ=Δl=mλ   *d=distance  between  slits   *solve  for  position  of  the  fringes   *it  is  negative  when  the  fringes  are  below  the  central  axis   *m=0,  (+/-­‐)  1,  (+/-­‐)  2…       -­‐bright  fringes  have  an  equation:  dsinθ=mλ       *m=0  is  the  central  maximum     -­‐dark  fringes  are  halfway  between  bright  fringes       *destructive     dsinθ=(m+(1/2))λ   *above  the  central   *m=1,2,3…     dsinθ=(m-­‐(1/2))λ   *below  the  central   *m=-­‐1,-­‐2,-­‐3…         *can  never  have  m=0     -­‐intensity       *decreases  because  light  intensity  of  each  slit  isn’t  the  same       *bright  fringes  are  equally  spaced       *greatest  at  m=0     y m(mλL)/d   *bright  fringes   *d=distance  between  slits   *L=distance  to  the  screen   *y=position  of  the  fringe  (interference  pattern)   *m=0,1,2,3…     y =(m+(1/2))(λL)/d   m *dark   *m=1,2,3…   *exactly  halfway  between  bright  fringes     3)  Interference  in  Reflected  Waves     -­‐if  there’s  reflected  waves,  they  can  interfere       *in  phase=constructive       *out  of  phase=destructive     -­‐from  higher  index  of  refraction  to  lower  index  of  refraction  has  no  phase     change     -­‐from  lower  index  of  refraction  to  higher  index  of  refraction  has  a  180  degree     phase  change     -­‐Constructive       (1/2)+(2d/λ)=m   *m=0,1,2…       -­‐Destructive     (1/2)+(2d/λ)=m+(1/2)       -­‐Thin  Film  Interference       *when  light  refracts  and  reflects  from  both  surfaces       *destructive  because  one  wave  has  change  and  one  doesn’t       *have  different  wavelengths  that  disperse  differently     λ nλ vacuum /n   *λ =wnvelength  in  the  medium       -­‐Destructive     2nt/λ vacuum =m   *t=thickness  of  the  film   *m=0,1,2…     -­‐Constructive     (2nt/λ vacuum )-­‐(1/2)=m   *m=0,1,2…       -­‐phase  change  depends  on  the  index  of  refraction  of  the  film  and  its     surroundings     4)  Diffraction  (single  slit)     -­‐wave  goes  through  a  barrier  with  a  width  (W)     -­‐the  wave  propagates  out     -­‐interference  patterns  from  different  sides  of  the  wave  have  diffraction     -­‐the  amount  of  diffraction  depends  on  the  wavelength     -­‐the  pattern  is  due  to  differences  in  the  path  length  from  different  parts  of  the     opening     -­‐Dark  fringes     Wsinθ=mλ   *W=width   *same  as  d  equation   *m=(+/-­‐)1…     5)  Resolution     -­‐microscopes  have  this     -­‐can  have  a  greater  resolution  depending  on  wavelengths     sinθ=1.22(λ/D)   *D=aperture  of  the  microscope       -­‐interference  patterns  block  out  the  picture     -­‐Rayleigh’s  criterion     6)  Diffraction  Grating     -­‐have  lots  of  parallel  slits  (N)       *could  be  hundreds     -­‐lots  of  light  bends     -­‐increase  the  number  of  slits,  have  less  constructive  and  more  destructive     interference       *peaks  become  narrower  and  more  intense       *dark  spaces  become  thicker     dsinθ=mλ   *Constructive  condition   *m=(+/-­‐)1,  (+/-­‐)2…   *if  given  lines/mm,  take  the  reciprocal  of  it     Chapter  29:  Relativity     1)  Postulates  of  Special  Relativity     -­‐Einstein  says  relativity  is  simple       *Equivalence  of  Physical  Laws=laws  of  motion  are  the  same  in  every         inertial  frame  of  reference  (inertial=constant  velocity)   8     *Constancy  of  the  Speed  of  Light=c=3X10 m/s  is  speed  of  light  in  a         vacuum  and  it  is  always  the  same     -­‐Non-­‐Inertial  Frames       *non-­‐inertial=having  acceleration  or  deceleration       *Earth  is  non-­‐inertial  but  the  acceleration  is  so  small  that  we  see  it  as         inertial       -­‐even  if  lights  are  moving  relative  to  each  other,  velocity  will  still  be  the     speed  of  light  in  a  vacuum         *c  is  a  constant  and  can’t  change       *in  order  to  have  this  work,  time  has  to  be  different  in  different         reference  frames  and  distance  has  to  change  when  we  are  in  different         reference  frames       *time  and  space  is  different  for  different  observers  in  different           reference  frames     -­‐Thomas  Young  proposed  that  light  has  to  travel  through  something       *light  must  travel  through  ether     -­‐Michelson  and  Morley  worked  to  detect  the  ether       *tested  c-­‐v  for  upwind  and  c+v  for  downwind       *thought  light  would  travel  differently  in  different  directions,  but  they       were  wrong  and  they  proved  c  is  constant     2)  Principle  of  Relativity     -­‐there’s  no  such  thing  as  absolute  rest       *showed  us  that  speed  of  light  in  a  vacuum  is  the  same  in  all  inertial         reference  frames     -­‐speed  of  light  is  the  ultimate  speed  limit  of  the  universe     3)  Time  Dialation     -­‐for  a  clock  at  rest,  time=Δt   0   Δt =2d/0   *Δt =Δt  when  velocity  is  zero   0 *Proper  Time       -­‐for  clock  in  motion  near  the  speed  of  light       *light  has  a  triangular  shape       *vertical  distance=d       *horizontal  distance=vΔt/2       *hypotenuse=cΔt/2       *have  two  distances,  Δx  and  Δx ,  for  each  tria1gle       *use  the  Pythagorean  theorem  to  solve  for  Δt     Δt=Δt /(√(1-­0β ))   2 *Δt =2d0c   *β=v/c   *time  dilation  equation       -­‐a  moving  clock  runs  slower       *as  speed  gets  closer  to  speed  of  light,  it  runs  slower       *for  any  clock/process  that  is  time  dependent     -­‐Event=a  physical  occurrence  at  a  specific  location  at  a  specific  time     -­‐Proper  Time=amount  of  time  separating  two  events  in  the  same  location       *THIS  IS  THE  KEY     -­‐all  physical  processes  (including  aging)  slow  down  as  you  approach  the       speed  of  light     -­‐it  has  been  measured  in  many  ways  including  through  subatomic  particles     -­‐consequence:  measuring  simultaneity  is  not  easy  to  do     4)  Length  Contraction     -­‐time  intervals  aren’t  absolute  because  of  time  dilation  equation  and  velocity     equation     -­‐Proper  Length=length  of  an  object  measured  in  the  reference  frame  when       the  object  is  at  rest     -­‐the  object  moving  is  less  than  proper  length=relativistic  length  contraction     L=√(1-­‐β L )   2 0 *L=observed  length   *L =p0oper  length       -­‐lengths  differ  because  space  is  different  in  two  reference  frames  moving     relative  to  each  other     -­‐length  contraction  takes  place  only  along  the  direct  of  motion     -­‐once  we  hit  0.6C  velocity,  the  lengths  drop  of  drastically     5)  Relativistic  Addition  of  Velocities     -­‐two  objects  moving  towards  each  other     v=(v +v )/11+((v v2)/c))   1 2 *relativistic  effect   *v=observed  speed     6)  Relativistic  Momentum     -­‐as  velocity  gets  closer  to  speed  of  light,  momentum  increases  without  limit     -­‐momentum=p=mv       *has  to  be  conserved       *as  objects  move  faster,  they  get  heavier     -­‐relativistic  momentum  is  conserved  in  all  collisions     -­‐relativistic  momentum  must  approach  classical  value  mv  as  v/c  gets  close  to     0     √(1-­‐β )=√(1-­‐(v /c ))=1   2 2     -­‐if  speed  of  the  object  is  less  than  0.1C,  classic  expression  will  equal  actual     momentum  within  5%     2 2 2 p=(mv)/√(1-­‐β )=(mv)/√(1-­‐(v /c ))  


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