total_internal_reflection

							Total internal reflection and critical angle




                                                                                       medium one

                                                                                       medium two
                                          c
                                                                     >c
            <c



                                  Critical angle                         Total internal reflection


                                                                                          Figure 1


When light passes from a material such as water into one of lower refractive index such as air it
is found that there is a maximum angle of incidence in the water that will give a refracted beam
in the air, that is, the angle of refraction is 90o. The angle of incidence in the denser medium
corresponding to an angle of refraction of 90o in the less dense medium is known as the critical
angle (c) (Figure 1). The reason for this is clear if we consider the formulae. For an angle of
refraction of 90o we have:
       2n1= sin i/ sin r = sin c/ sin 90 = 1/1n2


For light passing from a material of absolute refractive index n1 to one of absolute refractive
index n2 we have:

                              Critical angle (c):   n1sin c = n2

                       For n2 = 1, i.e air this becomes:   n1sin c = 1



 Example problem
 The refractive indices from air to glass and from air to water are 1.50 and 1.33 respectively.
 Calculate the critical angle for a water-glass surface.
 The refractive index for light passing from water to glass [wng] is given by
 wng = ng/nw = 1.5/1.33 = 1.13
 Therefore the critical angle (c) can be found from
 wng = 1/sin c   and so sin c = 1/1.13 = 0.89
 and so c = 62.5o




For an air-glass boundary, with n = 1.5, c = 42o and for an air-water boundary c = 48.5o


                                                                                                     1
For angles of incidence greater than the critical angle all the light is reflected back into the
optically more dense material, that is, the one with the greater refractive index. This is known as
total internal reflection and the normal laws of reflection are obeyed.
Total internal reflection explains the shiny appearance of the water surface of a swimming pool
when viewed at an angle from below. The phenomenon is used in prismatic binoculars
(Mirages are caused by continuous internal reflection.)

It is left as an exercise for you to prove that light cannot pass
across the corner of a right-angled glass block if the refractive
                                                                                             glass
index of the glass is 1.5 (see Figure 2).


The two photographs show this effect when attempting to look
across the corner of a right-angled fish tank.




            glass                                                                             Figure 2



                                      glass


                       air                            air




    water
                                              water

                Figure 3



This inability of light to pass across the corner of a right-angled
glass block when the block is in air is used in the depth gauge
shown in Figure 3. In diagram (a) the rod is in air and so the
light is reflected back to the top. In diagram (b) the rod is in
water which has a refractive index (1.33) closer to that of glass.
This will increase the critical angle and so light can escape in
to the water across the right angle.




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