The
index of refraction of the Earth’s atmosphere decreases
monotonically with height from its surface value
(about 1.00029) to
the value in space (about
1.000000 at the top of
the atmosphere. This
continuous (or graded)
variation can be approximated by considering
the atmosphere to be composed of three (or
more) plane parallel
layers in each of which the index of refraction is constant.
Thus, in
the figure,
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Solution: Click For PDF Version (a)We will use Snell’s law successively for answering this problem.
The angle of
refraction in the layer with refractive index
The angle of
refraction
The angle of
refraction
Combining these relations, we note that
(b)
We have to
calculate the shift in position of a star observed to be
For
and
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.
We will consider a ray of light from a star S
that strikes the top of the atmosphere at an angle
with the vertical. (a) We
have to show that the apparent direction
of the star with the vertical as seen by an observer at the Earth’s
surface is obtained from
from the vertical.
of the ray from the star incident on the top of the atmosphere at
incident angle
.
of the ray incident on top of the layer with refractive index
at angle
is given by the Snell’s law
.
at angle
.
,
,