Evolution of the Astronomical Eyepiece - Brayebrook Observatory

EVOLUTION of the ASTRONOMICAL EYEPIECE
Reflection losses may be quantified in terms of the refractive index gradient at the media
boundary, hence:
⎧ ⎪ ⎛
k = 1− µ − µ ⎞
1 2
⎨ ⎜ ⎟
⎩ ⎪ ⎝ µ 1 + µ 2 ⎠
2
⎫ ⎪ ⎧ ⎪
⎬
⎭ ⎪ 1 − ⎛ µ − µ ⎞
2 3
⎨ ⎜ ⎟
⎩ ⎪ ⎝ µ 2 + µ 3 ⎠
2
⎫ ⎪ ⎧
⎬
⎭ ⎪
........... ⎪
1 − ⎛ µ − µ ⎞
n−1 n
⎨ ⎜ ⎟
⎩ ⎪ ⎝ µ n −1 + µ n ⎠
2
⎫ ⎪
⎬
⎭ ⎪
for a cemented surface where:
µ 1
= µ 2
=1.5
(Canada balsam or Xylol)
and where:
µ 3
=1.7 k = 0.39%
µ 3
=1.8 k = 0.83%
µ 3
=1.9 k =1.38%
µ 3
= 2.0 k = 2.04%
and at an air-glass surface where:
µ 2
=1.0
µ 1
=1.5 k = 4.0%
µ 1
=1.6 k = 5.33%
µ = 1.7 k = 6.72%
µ 1
= 1.8 k = 8.16%
µ 1
= 1.9 k = 9.63%
µ 1
= 2.0 k =11.11%
It is therefore evident that reflection
losses from an air-glass surface are
greater than from a cemented surface,
but they also increase with the index
gradient. Because the refractive index
of glass changes with wavelength (dispersion),
r eflection losses vary across
the spectrum, which is why ghosts
often assume a specific hue.
Anti-r eflection coatings, developed in
the late 1930’s can virtually eliminate
reflection at air -glass surfaces. The
principle involved is the suppression of
the reflected incident ray by destructive
interf e rence, ba lanced by constructive
interference in the transmitted
pencil arising from reflection within
the film.
This can occur when the square of the
12
coating index equals the glass index,
the optical thickness of the film being a
quarter wave. Herein though lies the
first difficulty, for:
µ
f or crown a nd flint glass are
respectively 1.231 & 1.271, and
no solids have refractive indices as low
as this. Among the nearest are lithium
fluoride ( µ=1.39, reducing the loss from
between 4% - 5%, to a theoretical
0.1%,- nearer 1.5% in practice - over
the visual spectrum); calcium fluoride
(µ=1.34); sodium and magnesium fluorides;
m agnesium chl oride; silicon
dioxide (µ=1.46); cryolite and certain
fatty acids.
None of these are perfect: lithium fluoride
is fragile and soluble in water,
hence useless for outer surfaces;