Abstract

A Brewster polarizer in this study is any dielectric plane reflecting surface reflecting light at or near the Brewster angle of incidence. In this paper, we consider an interesting phenomenon observed when we use an extended source of light or a cone of light with its axis incident on the plane surface at the Brewster angle. The resulting reflected light is viewed (a) through an ordinary sheet polarizer and (b) after reflection from another Brewster polarizer. The extinction pattern of light by such a system is in the form of an elongated black shadow in (a) and a nearly circular shadow in (b), respectively. These shadows are explained on the basis and use of the familiar Fresnel equations at a plane interface between two dielectric media. Photographs of the shadows are also presented.

© 1983 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 (14)

Fig. 1
Fig. 1

Incident, refracted, and reflected rays at the plane interface of glass and air.

Fig. 2
Fig. 2

Cone of light is incident on the plane interface so that the axis of the cone is exactly at Brewster angle of incidence I0.

Fig. 3
Fig. 3

Spherical triangle and dihedral angle showing the relationship between the quantities I, I0, ϕ, ψ, ψ ¯, and α.

Fig. 4
Fig. 4

Polar diagram of intensity contours for the combination Brewster polarizer crossed-sheet analyzer.

Fig. 5
Fig. 5

Polar diagram of intensity contours for the combination Brewster polarizer parallel-sheet analyzer.

Fig. 6
Fig. 6

Schematic diagram showing how the intensity pattern is photographed.

Fig. 7
Fig. 7

Extinction pattern obtained for a Brewster polarizer and crossed-sheet analyzer.

Fig. 8
Fig. 8

Parallel position of two Brewster polarizers (ψ2ψ1 = 0).

Fig. 9
Fig. 9

Polar diagram of intensity contours for the situation as in Fig. 8.

Fig. 10
Fig. 10

Alternate parallel position of the Brewster polarizers ψ2ψ1 = π).

Fig. 11
Fig. 11

Polar diagram of intensity contours for the situation shown in Fig. 10.

Fig. 12
Fig. 12

Crossed position of two Brewster polarizers (ψ2ψ1 = π/2 or 3π/2).

Fig. 13
Fig. 13

Polar diagram of intensity contours in the case shown in Fig. 12.

Fig. 14
Fig. 14

Extinction pattern obtained for two crossed Brewster polarizers as shown in Fig. 12.

Equations (10)

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

R = tan 2 ( I I ) tan 2 ( I + I ) , R = sin 2 ( I I ) sin 2 ( I + I ) .
cos I = cos I 0 cos ϕ + sin I 0 sin ϕ cos ψ , cos ψ ¯ = ( cos ϕ cos I 0 cos I ) / sin I 0 sin I , tan α = cos I 0 tan ψ ¯ .
T x = R cos 2 α + R sin 2 α .
T = = R sin 2 α + R cos 2 α .
T = = R 2 + R 2
cos I 1 = cos I 0 cos ϕ + sin I 0 sin ϕ cos ψ 1 , cos I 2 = cos I 0 cos ϕ sin I 0 sin ϕ cos ψ 1 , cos ψ ¯ 1 = ( cos ϕ cos I 0 cos I 1 ) / sin I 0 sin I 1 , cos ψ ¯ 2 = ( cos ϕ cos I 0 cos I 2 ) / sin I 0 sin I 2 , tan α 1 = cos I 0 tan ψ ¯ 1 , tan α 2 = cos I 0 tan ψ ¯ 2 . }
T = = [ R ( 1 ) cos 2 α 1 + R ( 1 ) sin 2 α 1 ] [ R ( 2 ) cos 2 α 2 + R ( 2 ) sin 2 α 2 ] + [ R ( 1 ) sin 2 α 1 + R ( 1 ) cos 2 α 1 ] [ R ( 2 ) sin 2 α 2 + R ( 2 ) cos 2 α 2 ] .
cos I 1 = cos I 0 cos ϕ + sin I 0 sin ϕ cos ψ 1 , cos I 2 = cos I 0 cos ϕ sin I 0 sin ϕ sin ψ 1 ,
cos I 1 = cos I 0 cos ϕ + sin I 0 sin ϕ cos ψ 1 cos I 2 = cos I 0 cos ϕ + sin I 0 sin ϕ sin ψ 1 .
T x = [ R ( 1 ) cos 2 α 1 + R ( 1 ) sin 2 α 1 ] [ R ( 2 ) sin 2 α 2 + R ( 2 ) cos 2 α 2 ] + [ R ( 1 ) sin 2 α 1 + R ( 1 ) cos 2 α 1 ] [ R ( 2 ) cos 2 α 2 + R ( 2 ) sin 2 α 2 ] .

Metrics