We know from the foregoing that the denominator of the cone reflectance has at least one root at . We now investigate the ``dc behavior'' more thoroughly.

- A hasty analysis based on the reflection and transmission filters (see figure) might conclude that the reflectance of the conical cap converges to at dc, since and . However, this is incorrect.
- Instead, it is necessary to take the limit as
of
the complete conical cap reflectance
:
- To find the reflectance at dc, we may use L'Hospital's rule to obtain
- We apply L'Hospital's rule again to obtain
- From a physical point of view, it makes more sense that the cone should
``look like'' a simple rigid termination of the cylinder at dc, since its
length becomes vanishingly small compared with the wavelength in the limit.
- Another method of showing this result is to form a Taylor series expansion
of the numerator and denominator:

Both series begin with the term which means both the numerator and denominator have two roots at . Hence, again the conclusion is two pole-zero cancellations at dc.

- The series for the conical cap
reflectance is

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