Abstract

This paper presents an analysis of the para-elliptic reflector together with its possible applications when used as a searchlight mirror. The horizontal sections of a para-elliptic mirror are portions of ellipses and the vertical sections are parabolas. The mirror is so designed that each parabola lies in a vertical plane through the secondary focus of the horizontal ellipse which passes through the vertex of the mirror and each elliptical section lies in a plane parallel to that of the ellipse through the vertex of the mirror. A beam of light projected from such a reflector converges in the horizontal planes to a line common to the intersection of the vertical planes and then diverges as a spread beam horizontally with minimum spread vertically.

© 1949 Optical Society of America

Full Article  |  PDF Article

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

F. 1
F. 1

Beam produced by mirror which is a segment of ellipsoid of revolution.

F. 2
F. 2

Type of beam produced by a para-elliptic mirror.

F. 3
F. 3

Illustration of the elements of a para-elliptic reflector with a system of coordinates having origin at center of the ellipse through the optical axis.

F. 4
F. 4

Illustration of para-elliptic mirror with focal length of 12 inches, short diameter 20 inches, and angle of convergence of 17 degrees.

F. 5
F. 5

Plot of the RR1 values against the distance from the center of the specific para-elliptic reflector resulting from the assumed dimensions and angle of convergence.

F. 6
F. 6

Variation of the focal lengths of the parabolas in passing from the center to the edge of the specific para-elliptic reflector resulting from the assumed dimensions and angle of convergence.

F. 7
F. 7

Variation of the distance from the light source to the parabolas in passing from the center to the edge of the specific para-elliptic reflector resulting from the assumed dimensions and angle of convergence.

Tables (1)

Tables Icon

Table I Evaluation of “f” values of y1 from 1 through 9.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

x 2 / a 2 + y 2 / b 2 = 1
z 2 = 4 ( F S ) ( x + a ) .
z 1 2 / ( N A ) 2 + y 1 2 / ( U A ) 2 = 1 .
( P R 1 ) 2 = 4 f ( R R 1 )
z 1 2 = 4 f ( R R 1 ) .
R R 1 = F 1 R F 1 R 1 .
F 1 T = 2 a F 1 D S T ;
F 1 T = 2 a F S ( a x ) = a F S + x .
F 1 T = m + x
F 1 A = 2 a F 1 D S A ;
F 1 A = n
R R 1 = [ ( m + x ) 2 + y 2 ] 1 2 ( n 2 + y 2 1 ) 1 2 .
y 1 / y = F 1 A / F 1 T = n / m + x .
y = 2 m n / y 1 ± [ 4 m 2 n 2 / y 1 2 4 ( n 2 / y 1 2 + a 2 / b 2 ) ( m 2 a 2 ) ] 1 2 2 ( n 2 / y 1 2 + a 2 / b 2 )
Tan . 8 1 2 ° = 10 / 2 a F S S A = 10 / 2 a 12 2.521 a = 40.716 inches ;
2 m n y 1 + [ 4 m 2 n 2 y 1 2 4 ( n 2 y 1 2 + a 2 b 2 ) ( m 2 a 2 ) ] 1 2 2 ( n 2 y 1 2 + a 2 b 2 ) = y
n y y 1 m = x 66.911 y y 1 28.716 = x
( 1 y 1 2 ( 10 ) 2 ) ( 11 ) 2 = z 1 2
z 1 2 4 ( R R 1 ) = f