PHYS  1540                                                                                                                                                                                                4/12/2014              

   

Experiment  11          

Reflection,  Refraction,  Dispersion    of  Light  and  Brewster’s  Angle  

                           

Christopher  Douglas      

   

Introduction    

Experiment  11  consisted  of  four  individual  experiments  that  each  involved  various  

topics  within  the  branch  of  physics  generally  known  as  optics.  The  first  experiment  

dealt  with  the  connection  between  the  angle  of  incidence  and  the  angle  of  reflection  

as  applied  to  light  rays  interacting  with  mirrors  of  various  geometrical  shapes.  The  

second  experiment  examined  some  of  the  same  principles  however  instead  of  the  

use  of  mirrors,  the  light  ray  was  passed  through  a  lens  and  refraction  was  analyzed.  

The  third  experiment  observed  the  phenomenon  of  dispersion  by  passing  a  light  ray  

through  an  acrylic  rhomboid.  Once  the  light  ray  passed  through  the  rhomboid,  

various  calculations  were  made  relating  to  the  indices  for  each  unique  color  the  ray  

produced.  Our  last  experiment  introduced  Brewster’s  Angle  by  exploring  

polarization  and  the  use  of  polarizing  lenses.  

 

Theory  A:  Reflection  

As  a  ray  of  light  lands  and  hits  a  specific  point  on  a  perfectly  flat  mirror,  the  light  

“rebounds”  or  reflects  from  that  point.  This  incoming  ray  is  referred  to  as  the  

incident  ray  and  the  light  that  “bounces”  off  the  point  is  called  the  reflected  ray.  

When  the  incident  ray  makes  it’s  initial  strike  on  the  mirror,  a  line  normal  to  that  

point  can  be  drawn  perpendicular  to  the  light  ray.  On  the  side  of  the  normal  line  that  

encompasses  the  incident  ray,  the  angle  of  incident  can  be  measured  between  the  

normal  and  the  incident  ray  itself.  As  one  might  expect,  the  angle  of  reflection  

between  the  normal  and  the  reflection  ray  can  be  measured  in  much  the  same  way.  

When  these  two  angles  are  measured,  we  see  they  are  equivalent.  These  two  angles  

being  equal  verifies  the  law  of  reflection  which  tells  us  that  the  angle  of  incidence  is  

equal  to  the  angle  of  reflection,  Θr  =  Θi.  

 

The  Angular  Relationship  Between  the  Incident  and  Reflected  Light  Rays    

       

   

       

   

Equipment  List    

• Ray  Optics  Kit  • Basic  Optics  Light  Source  • Protractor  • Ruler  • White  Paper  • Pencil  • D-­‐Shaped  Acrylic  Lens  • Polarize  

     

 Note:  The  above  equipment  list  applies  to  all  four  experiments  included  in    

                       lab  11.  

 

Procedure  A:  Reflection    

The  procedure  began  by  tracing  the  three-­‐way  mirror  on  a  sheet  of  white  paper.  The  

halfway  point  on  the  straight  end  of  the  mirror  was  marked  and  the  normal  line  was  

drawn  from  the  apex  on  the  opposite  end  through  the  mark  and  beyond  to  about  10  

centimeters.  This  step  was  then  repeated  for  the  remaining  two  sides.  

 

Drawing  Normal  Lines  

     

     

 

 

 

Once  all  normal  lines  were  drawn,  the  light  source  was  directed  at  each  side  such  

that  the  beam  hit  the  point  where  the  normal  line  protrudes.  The  light  source  being  

directed  towards  the  mirror  produced  an  incident  ray  and  a  reflected  ray,  these  rays  

and  their  respective  angles  were  each  marked  and  measured  carefully  with  a  

protractor  and  ruler.  

 

 

 

Completed  Three-­‐Way  Mirror  Angle  Analysis    

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

Note:  A  lab  partner  held  the  three-­‐way  mirror  down  while  the  tracing  was    

                       performed.  This  prevented  the  mirror  from  slipping  out  of  place  which  in  turn            

                       may  yield  inaccurate  data.  

 

 

Data  A:  Reflection  

 

 

 

 

Analysis  A:  Reflection  

As  expected,  the  angles  of  incidence  were  equal  to  the  angles  of  reflection.    The  law  

of  reflection,  which  shows  Θi  =  Θr,  was  verified.  As  each  side  was  analyzed,  it  was  

determined  that  the  magnitude  of  each  angle  was  different  based  upon  the  

geometry  of  the  side  itself.  The  concave  side  of  the  mirror  produced  angles  that  

were  slightly  smaller  than  both  and  straight  and  convex  sides.  Naturally  the  same  

trend  was  observed  for  the  convex  and  straight  sides  respectively.  

 

Theory  B:  Refraction  

Refraction  is  a  phenomenon  studied  in  many  braches  of  science.  In  the  branch  of  

physics  termed  optics,  refraction  is  a  surface  phenomenon  that  simply  refers  to  the  

bending  of  light  due  to  its  passing  through  different  material  mediums.    When  light  

travels  through  air  then  suddenly  strikes  and  passes  through  glass  for  instance,  the  

light  ray  slows  down.  The  consequence  of  this  change  in  the  material  medium  

causes  the  light  to  bend.  The  degree  to  which  the  light  slows  down  is  indicated  by  

“n”  or  the  index  of  refraction.  The  higher  the  index,  the  greater  the  light  will  

decrease  in  speed.  The  angles  generated  by  this  change  in  speed  and  direction  can  

be  found  with  Snell’s  Law:  

n1sin(Θ1)=n2sin(Θ2)  

 

The  above  equation  shows  us  that  n1  (the  incident  material  index)  times  the  

incident  angle  is  equal  to  n2  (the  refraction  material  index)  times  the  angle  of  

refraction.    

 

Procedure  B:  Refraction  

The  light  source  was  placed  on  the  lab  table  and  adjusted  to  produce  a  single  beam  

of  light.  The  light  source  was  then  carefully  maneuvered  such  that  the  light  passed  

directly  through  the  middle  of  the  ray  table  at  0°.  The  lens  shaped  like  a  capital  “D”  

was  placed  on  the  center  of  the  ray  table.  The  ray  table  was  calibrated  to  the  0°  

mark,  as  relating  to  the  angle  of  incidence.  The  angles  of  refraction  were  carefully  

measure  and  recorded.  Assembly  seen  below:  

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

Note:  While  adjusting  the  light  source,  the  rotation  of  the  ray  table  proceeded    

                       slowly.  It  was  determined  that  rushing  the  rotation  of  the  ray  table  lead    

                       to  inaccurate  data.  

 

Data  B:  Refraction  

 

 

Analysis  B:  Refraction  

After  all  the  data  was  recorded,  the  index  of  refraction  was  found  by  using  Snell’s  

Law.  The  given  angles  and  indices  selected  to  plug  into  the  Snell’s  Law  equation  

were  n1=1.0  (index  in  air),  Θi=50°  and  Θr=31°.  The  result  gave  an  index  of  refraction  

for  the  lens  of  n2=1.48.  This  result  was  proven  successful  in  that  only  0.23%  error  

was  found  when  comparing  the  experimental  index  to  the  theoretical  index.    

 

 

Theory  C:  Dispersion  

We  have  all  seen  a  prism  or  looked  up  in  the  sky  to  witness  the  beauty  of  a  rainbow.  

On  he  other  hand,  all  of  us  have  enjoyed  the  sunlight  or  the  convenience  of  an  

ordinary  bedside  lamp.  This  ordinary  light  we  see  throughout  our  daily  lives  is  often  

times  referred  to  as  “white  light.”  White  light  is  simply  light  that  is  a  combination  of  

several  different  colors  that  each  have  a  unique  wavelength.  With  careful  precision,  

one  can  actually  separate  out  all  different  colors  through  refraction  and  see  each  

individual  color  generated  by  it  respective  wavelength.  This  process  of  separation  

by  refraction  is  called  dispersion.  

Procedure  C:  Dispersion  

An  acrylic  rhomboid  was  placed  on  a  white  sheet  of  paper  and  carefully  traced  

around  its  outside  perimeter.  The  rhomboid  was  lifted  off  the  paper  and  a  normal  

line  was  drawn  from  the  angled  side  along  with  another  line  45°  from  the  normal.  

The  light  source  was  then  directed  through  the  normal  line.  The  light  ray  entering,  

exiting  and  the  dispersion  trends  were  all  traced  and  labeled.  As  the  light  ray  existed  

through  the  paper,  dispersion  of  blue  and  red  light  was  observed.  The  angles,  

indices  of  refraction  and  velocities  of  the  dispersion  were  measured.  

   

 

 

 

 

Data  C:  Dispersion  

 

 

Analysis  C:  Dispersion  

The  angles  were  found  using  a  protractor,  the  indices  were  calculated  using  Snell’s  

Law  and  the  velocities  were  proven  by  knowing  that  the  index  is  equal  to  the  speed  

of  light  divided  by  the  velocity,  n=c/v,  where  c=3.00x10^8  m/s.  Equations  below:  

 

 

 

 

 

 

 

Theory  D:  Brewster’s  Angle  

When  light  bearing  a  specific  polarity  travels  through  a  transparent  dielectric  

surface  and  results  in  no  reflection,  the  angle  at  which  it  enters  (angle  of  incidence)  

is  commonly  referred  to  as  Brewster’s  Angle.  This  angle  can  be  found  with  relative  

ease  with  a  polarizing  disk  and  by  simply  locating  the  angle  where  the  refracted  and  

reflected  rays  are  separated  by  90°.  

 

Procedure  D:  Brewster’s  Angle  

The  lens  with  the  shape  of  a  capital  “D”  was  placed  on  the  ray  table  and  the  light  

source  was  directed  at  the  center  of  the  table  and  straight  side  of  the  lens.  The  ray  

table  was  rotated  while  being  observed  through  a  polarizing  disk.  The  ray  table  was  

then  positioned  at  an  angle  of  90°  separation  between  the  refracted  and  reflected  

rays.  The  polarizing  disk  was  rotated  until  the  light  intensity  diminished.  This  angle  

was  the  marked  and  calculated.      

 

Data  D:  Brewster’s  Angle  

 

 

 

 

 

 

Analysis  D:  Brewster’s  Angle  

By  again  using  Snell’s  Law,  Brewster’s  Angle  was  observed  after  a  few  careful  

calculations.  Though  some  substitutions  had  to  be  done  in  order  to  derive  our  

needed  equation,  after  the  derivation  was  complete,  our  needed  angle  was  found.  

See  below  for  the  derivation:  

 

 

 

 

 

 

 

 

Discussion  of  Results  

Throughout  each  experiment,  the  laws  governing  reflection,  refraction,  dispersion  

and  Brewster’s  Angle  were  rigorously  tested  and  ultimately  verified.  The  Law  of  

reflection  was  verified  by  our  angle  of  incidence  being  equal  to  the  angle  of  

reflection.  We  saw  in  the  refraction  experiment  that  as  the  index  of  refraction  

increased,  the  speed  decreased  and  this  was  verified  with  Snell’s  Law  and  the  

velocity  equation.  By  measuring  the  angles,  speeds  and  indexes  of  the  dispersed  

light  through  the  acrylic  rhomboid,  the  principles  of  dispersion  were  upheld.  

Brewster’s  Angle  was  found  and  also  verified  with  the  use  of  the  ray  table  by  placing  

the  refraction  and  reflected  rays  90°  apart,  then  observing  with  the  polarizing  lens.  

The  principles  that  guide  each  phenomenon  were  analyzed  and  were  verified  

without  exception.  

 

Conclusion  

Overall,  the  experiments  were  a  success.  I  felt  as  though  my  lab  partners  and  myself  

actively  engaged  in  each  procedure  and  learned  the  concepts  that  were  presented.  

Some  mechanical  error  can  be  found  due  impart  by  the  dispersion  of  the  light  source  

at  the  ends  of  its  produced  rays.  Human  error  can  be  found  in  instances  where  the  

three-­‐way  mirror  was  “bumped”  accidentally,  slightly  altering  the  measured  angle.  

Although  error  was  present,  the  overall  statistical  data  was  not  greatly  affected  as  

can  be  seen  by  the  minimal  percent  error  and  expected  results.  I  enjoyed  this  lab  

very  much,  I  felt  as  though  it  increased  my  understanding  of  the  presented  material  

and  exposed  me  to  the  reliable  methods  behind  accurate  science.    

 

 

 

 

 

 

 

 

 

 

Work  Cited  

 

University  of  North  Texas  Physics  Department.  General  Physics  1540  with  Calculus    

  Lab  II.  Denton:  Eagle  Image  Digital  Print  Centers,  2013.  Print.