1.2.6 Total internal reflection by pharmphresh30

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									1.2.6 Total internal reflection

Benson 35.4, p. 715


                    light ray starts in
                optically denser medium

Snell's law:     n1 sin q1 = n2 sin q2 and n1 > n2,

                 so sin q2 > sin q1, so q2 > q1


                         angle of refraction is greater
                           than angle of incidence

                                q2
           n2
                                        e.g. air

        n1 (> n2)                       water

    "optically denser"     q1
         medium
  the angle of incidence can be increased to a
  point when the angle of refraction becomes so
  great that the refracted ray grazes along the
  interface:
           n                     q2 = 90∞
            2



           n1                    q1 = qc


                             "critical angle"
                     1


n1 sin qc = n2 sin 90∞      so        sin qc = n2 / n1


 if the angle of incidence is increased any further,
 no light gets refracted; instead all the light gets
 reflected: total internal reflection
          n2


          n1
                     q1          q1
                   (> qc)
Example:
                                           water surface




                                      2 the entire world
                                     around you appears
                                         in this circle!

             1 look up from under water

Note: in almost all cases of refraction some light
gets reflected (in the case of total internal reflection
all of it; total internal reflection reflects close
to 100% of the incident light, metal mirrors
only about 90%)
                                   refracted light
                               q2
        n2


      n1            q1      q1



                         some reflected light
 1.2.7 Optical fibres & prism reflectors
 Benson p. 716/717                   optically dense
                          10-50mm
                                    material (e.g. glass)
incoming
light ray




   total internal               light ray has been
    reflections                 "guided" by fibre
extremely important to transmit information
because of much higher capacity than electrical wires
(lots of different colours at once!)

also used, for example,
in endoscopes:
                                        "coherent fibre
 each fibre transmits                      bundle"
one "pixel", the bundle
 as a whole transmits
    an entire image

            pixels
Prism reflectors

Benson p. 716




                         prism reflector;
                         very high reflectivity!


        reflected light ray

used, for example, in binoculars (to flip the image)
1.2.8 Dispersion & prisms

Benson 35.5, p. 717

the refractive index, n, is (slightly) different
for different colours


e.g. refractive index of glass
       n


1.52

1.5

1.48


              400             700     l [nm]

                    visible
                    range                 wavelength
           violet                   red
            functions of the wavelength, l
Snell's law:

         n1 sin q1 = n2(l) sin q2(l)

      different refractive indices lead to
        different angles of diffraction

     incident white
        light ray

                  q1
    n1

                            q2(red)
   n2(l) q2(blue)
                                 red
                                  lig
                       blue



                                      ht
                                       ray
                            l
                         ight
                           ray




                       white light is "split" into
                        its colour components
diffractive "slab":

Benson p. 718

                incident white
                   light ray
         n1


       n2(l)


         n1
                                 blu gre red
                                    e en


                          displaced, but parallel
dispersion prism:

Benson p. 718                         angle of
                               n1     deviation
  incident white
     light ray
                                      d

                n2(l)                            red

                                          bl
                                            ue

                        rays with different colours
                         have different directions!


   used in spectrometers (measure d, infer l)

								
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