In
the figure cross section has been shown of a hollow glass tube of
internal radius r, external
radius R, and index of
refraction n. (a) We
have to convince ourselves that the ray ABC shown in the figure
defines the apparent internal radius
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Solution: Click For PDF Version To an observer facing the hollow glass tube the size of the inner part of the glass tube will be determined by the parallel rays as shown in the figure. The apparent internal radius
will be the perpendicular distance between the ray BC
and a parallel ray passing through the
axis.
We use the
Snell’s law of refraction and the geometry of the line drawing
for calculating
Let
We have
From the figure we note that
and
Substituting these results in the refraction equation, we get
which is
independent of R.
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,
and is independent of R.
be the angle of incidence that the ray AB tangential to the inner
surface of the tube make with the external surface of the tube. Let
be the angle of refraction.
,
.