Physics for Geologists, Second edition

39 40 41 42 43
Angle from centre of rainbow
Optics 55
Figure 4.8 Angles of light scattered back from a raindrop. The proportion of
the radius at entry is the sine of the angle of incidence, so the cusp
of the curve, where the scattered light is most concentrated, comes
from the rays with an angle of incidence between about 58" and 60".
colours of different frequencies and wavelengths are refracted at slightly
different angles, as from a prism. The red is returned at an angle of about
43", while the violet is returned at an angle of about 40.5" - putting red on
the outside of the rainbow, and violet on the inside.
This is what Descartes found. The only difference is that he would have
taken very much longer to draw his lines.
Rainbows can only be seen by an observer on flat ground when the sun is
low in the sky, beginning with an elevation of less than 40". Standing on top
of the Matterhorn, rainbows can be seen when the sun is higher, and they
can be more complete with your shadow at the centre. A complete circle can
be seen from an aeroplane, when the shadow of the aeroplane is at the centre
of the circle.
The light reflected at the exit point of the primary rainbow and refracted at
the next internal surface sometimes gives rise to another but weaker rainbow
at about 52". In this one, the colours are reversed because of the second
internal reflection.
Stereoscopy
We see things in three dimensions because our brain has the capacity to
fuse the image each eye receives into one, each eye seeing a slightly different
image from its slightly different position. Use is made of this in binoculars,
binocular microscopes and in the making of maps from aerial photographs.
Photographs are taken sequentially from an aircraft flying at a constant
height with the camera pointing vertically downwards, with about 60 per
cent overlap between photographs. Adjacent pairs can be viewed stereo-
scopically through a stereoscope (see Figure 4.9), and a 3-D image of the
common ground in the two photographs is seen. It is as if one eye was in the
position from which the first photograph was taken, the other in the next.
Copyright 2002 by Richard E. Chapman