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8.3  -­‐  Critical  Angle,  Total  Internal  Reflection  and  Electromagnetic  Radiation  Critical  angle  and  total  internal  reflection  When  light  is  incident  upon  the  boundary  between  two  media,  reflection,  transmission  and  absorption  may  occur.    

Light  travelling  from  water  into  air  • As  the  angle  of  incidence  is  increased,  the  angle  of  refraction  also  

increases.    • This  continues  until  the  angle  of  refraction  will  be  almost  90  and  

the  transmitted  ray  travels  just  along  the  surface  of  the  water  • This  incident  angle  is  called  the  critical  angle,  ic,  • The  critical  angle  can  be  found  for  any  boundary  between  two  

media  by  using  Snell’s  law.  

If  the  incident  angle  is  equal  to  the  critical  angle,  i.e.  i=  ic  ,  then  r=  90.    Then  Snell’s  law  becomes  

𝑠𝑖𝑛  𝑖!𝑠𝑖𝑛90

=𝑛!𝑛!  

sin 𝑖! =𝑛!𝑛!  

 The  critical  angle  for  light  travelling  from  water  into  air  is  approximately  49o.  

If  the  incident  angle  is  greater  than  49o  total  internal  reflection  occurs.  

 

Worked  example  8.3A  An   underwater   light   shines   upwards   from   the   centre   of   a   swimming   pool   that   is   1.50   m   deep.  Determine  the  radius  of  the  circle  of  light  that  is  seen  from  above.  (nair  1.00,  nwater  1.33)  

 

Total   internal   reflection   is   used   in   many   optical   instruments,   including   cameras,   periscopes   and  binoculars.  When  light  reflects  from  a  mirror  there  is  always  some  loss  in  the  intensity  of  the  incident  light,  and  reflection  can  occur  from  both  the  front  and  rear  surfaces  of  the  mirror,  causing  problems.  By  contrast,  almost  no  loss  of  intensity  occurs  with  total  internal  reflection.  Since  the  refractive  index  for  glass  is  about  1.5,  the  critical  angle  for  light  travelling  from  glass  to  air  is  approximately  42,  and  a  glass  prism  with  internal  angles  of  45  can  be  used  as  a  mirror  in  the  applications  discussed  above.    

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Electromagnetic  waves  

1860s   investigations   being   carried   out   on   different   forms   of  electromagnetic   radiation   led   to   the  finding  that  visible  light  itself  is  just  one  of  the  many  forms  of  electromagnetic  radiation  (EMR)  

Electricity   and  magnetism  were   once   considered   to   be   separate   subjects.   However,  moving   charges  create  magnetic  fields.  Similarly  a  changing  magnetic  field  can  be  used  to  create  electricity.    

In   1864   James   Clerk   Maxwell   used   mathematical   equations   to   describe   how   charges   moving  periodically   in  a  conductor  would  set  up  alternating  electric   fields  and  magnetic   fields   in   the  nearby  region.    

Maxwell   knew   that   the  magnetic   and   electric  fields  travelled  through  space.   He   calculated  their   speed   and   found  it  to  be  300  000  km  s-­‐1,  exactly  the  same  as  the  speed  of  light!    

Also,   he   devised  mathematical  expressions  to  describe  the   magnetic   and  electric   fields.   The  solution   to   these  expressions   was   found  to   be   the   equation   of   a  wave.  Maxwell  had  shown  that  light  is  an  electromagnetic  wave.  

Today   we   know   that   the   electromagnetic   spectrum   includes   a   wide   range   of   frequencies   (or  wavelengths).  All  electromagnetic  waves  are  created  by  accelerating  charges  which  result  in  a  rapidly  changing  magnetic  field  and  electric  field  travelling  out  from  the  source  at  the  speed  of  light,  as  shown  in  Figure  8.35.  

The   many   forms   of   EMR   are   essentially   the   same,   differing   only   in   their   frequency   and,  therefore,  their  wavelength.    

 

The   electromagnetic   spectrum   is   roughly   divided   into   seven   categories   depending   on   how   the  radiation   is   produced   and   the   frequency.   The   energy   carried   by   the   electromagnetic   radiation   is  proportional   to   the   frequency.  High-­‐frequency   short-­‐wavelength  gamma  rays  are  at   the  high-­‐energy  end  of  the  spectrum.  Low-­‐frequency  long-­‐wavelength  radio  waves  carry  the  least  energy.  Humans  have  cells  in  their  eyes  which  can  respond  to  EMR  of  frequencies  between  approximately  400  THz  and  800  THz;  these  frequencies  make  up  the  visible  light  section  of  the  electromagnetic  spectrum.  

 

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Coloured  light,  different  wavelengths  

Our   eyes   are   responsive   to   many   different   colours   of   light   from   the   deepest   red   through   to   the  brightest  violet,  the  visible  spectrum  (Figure  8.37).    

Each  variation  in  colour  or  shade  is  caused  by  light  of  a  different  wavelength.    

Traditionally   the   colours  quoted  as  making  up   the  visible   spectrum   are   red,   orange,   yellow,   green,  blue  and  violet.  However,  as  shown  in  Figure  8.37,  the   actual   allocation   of   separate   names   for   the  colours   is   difficult   since   they   merge   into   one  another.    

The   wavelengths   associated   with   visible   light   are  very  small:  they  range  from  approximately  390  nm  (or   390x10-­‐9  m)   for   violet   light   to   around  780  nm  for  red  light.    Colour  addition  or  mixing  light  sources  Red,  green  and  blue  (RGB)  are  called  the  primary  colours  of  light.  None  of  the  primary  colours  can  be  produced  by  a  combination  of  the  other  primary  colours.    

 

 

 

 

                 

 Figure  8.39  shows  the  three  primary  colours  of  light  overlapping  to  produce  other  colours.  The  particular  colours  formed  by  the  overlapping  of  pairs  of  primary  colours  are  called  cyan,  magenta  and  yellow.  Any  group  of  colours  which  combine  to  form  white  light  are  called  complementary  colours.  All  three  primary  colours  when  combined  form  white  light.  Combining  any  two  primary  colours  forms  the  complementary  colour  of  the  remaining  primary  colour.  So,  for  example,  when  red  and  green  are  combined  they  form  the  complement  of  blue,  which  is  yellow.  Yellow  is  the  complement  of  blue.  Cyan  is  the  complement  of  red,  and  magenta  is  the  complement  of  green.    

     

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8.4  Dispersion  and  Polarisation  of  light  waves  

• White   light   is  made  up  of  many  different   frequencies  

(colours)  of  light.    

• For   some   materials   the   speed   at   which   light   is  

transmitted   is   actually   slightly   different   for   different  

frequencies  (colours)  of  light.    

• This  means  that  on  refraction  different  colours  of  light  

will   take   slightly   different   paths.   This   results   in   the  

spreading   out   of   the   white   light   into   its   component  

colours.    

• This  is  called  the  dispersion  of  white  light.  

As  light  enters  a  prism,  it  refracts  due  to  a  change  in  speed.  Why  does  light  slow  down  when  it  

enters  a  more  optically  dense  medium?    

The  light  energy  is  being  momentarily  absorbed  and  then  re-­‐radiated  by  the  atoms  that  make  

up  the  medium.  Different  colours  of  light  interact  differently  with  these  atoms.  As  a  result  they  

travel  at  different  speeds  within  the  medium  and  so  are  refracted  through  different  angles.    

Of  the  colours  in  the  visible  spectrum:  

• Violet  light  is  slowed  down  the  most  and  so  is  refracted  through  the  greatest  angle.    

• Red  light  is  slowed  least  and  so  is  refracted  the  least.  

 

Polarisation  

Further  evidence  for  the  wave  nature  of  light  is  the  

finding  that  light  can  be  polarised.  

Techniques  for  polarising  light  

The  most  familiar  way  in  which  unpolarised  (non-­‐

aligned)  light  can  be  converted  to  polarised  (aligned)  

light  is  by  using  polarising  filters.  

 

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The  fact  that  light  can  be  polarised  provides  strong  evidence  that  light  is  actually  a  transverse  

wave  since  longitudinal  waves  cannot  be  polarised.  

 

 

 

How  Polaroid  sunglasses  work  

When  outdoors  on  a  bright,  sunny  day,  the  smooth,  highly  

reflective,  horizontal  surfaces  around  you  are  a  significant  

contributor  to  the  amount  of  light  entering  your  eyes.  Bring  

to  mind  the  glare  that  can  occur  from  the  surface  of  water  

or   snow.   Fortunately   light   that   is   reflected   from   smooth,  

horizontal   surfaces   tends   to   be   polarised   (aligned)   in   a  

horizontal   direction.   An   appropriately   orientated  

polarising   filter   can   be   used.   Lenses   in   a   pair   of   Polaroid  

sunglasses   are   polarising   filters   orientated   to   block   the  

horizontal   wave   components,   allowing   only   vertical   components   through.   Hence   the   intensity   of  

light—that  is,  the  glare—is  markedly  reduced.