Abstract

This paper describes a reflecting sight in which a mirror objective is used instead of a usual lens. The instrument becomes very small and the optical element is simple even for a large field of view. The astigmatism produced by the oblique reflecting plate is compensated by an off-center cylindrical lens. The problem is mathematically solved.

© 1947 Optical Society of America

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References

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  1. Svenska Ackumulator AB Jungner, Stockholm, Sweden.
  2. Elementary Optics, , (1921).
  3. Swedish patent No. 116965.

Other (3)

Svenska Ackumulator AB Jungner, Stockholm, Sweden.

Elementary Optics, , (1921).

Swedish patent No. 116965.

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Figures (8)

F. 1
F. 1

Common reflecting sight with a lens f:2.

F. 2
F. 2

Reflecting sight distorted by a mirror.

F. 3
F. 3

Reflecting sight with an objective f:0.8.

F. 4
F. 4

Nife reflecting sight, first model.

F. 5
F. 5

Optics of the new sight with the Mangin mirror and decentered cylindrical lens.

F. 6
F. 6

Rays emanating from point 0 are afflicted by different astigmatism, increasing from zero for a ray perpendicular to the plate with thickness e.

F. 7
F. 7

Astigmatism in a slight prism is a function of the angle of incidence.

F. 8
F. 8

Astigmatism in a cylindrical lens.

Equations (16)

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s t = e 1 n 2 n tan 2 i cos i .
d ( s t ) / d i = e 1 n 2 n 2 sin i cos i ( 3 cos 2 i ) cos 5 i .
s t = 0.27 e , d ( s t ) / d i = 0.76 e .
s 2 t 2 = ( n 2 1 ) m sin υ sin ( 2 i 1 + υ ) cos 3 i 1 cos 2 i 2 + 1 n 2 n [ d 0 cos υ m tan i 1 sin υ ] sin 2 i 2 cos 3 i 2 .
s 2 t 2 = ( n 2 1 ) ( m d 0 / n ) tan 2 υ ,
d ( s 2 t 2 ) / d i 1 = 2 ( n 2 1 ) / n × ( m d 0 / n ) tan υ ( 1 + 3 2 tan 2 υ ) .
s 2 t 2 = 1.3 ( m d 0 / n ) tan 2 υ , d ( s 2 t 2 ) / d i 1 = 1.7 ( m d 0 / n ) tan υ .
s t = p 2 / ( f p ) ,
s t = ( ( n 1 ) / r ) p 2 .
1.7 ( m d 0 / n ) tan υ = 0.76 e ,
( m d 0 / n ) tan υ 0.445 e = 0 .
0.27 e 1.3 ( m d 0 / n ) tan 2 υ [ m ( d 0 + d ) / n ] 2 ( n 1 ) / r = 0 .
d + d 0 + 1 2 r sin 2 υ ,
x = 2 f 2 / ( s t ) .
tan ψ = ( s t ) ϕ / 2 f 2 .
d ( s t ) / d i = 0.76 e ,