Abstract

In this paper an account of the production of the color fringes in photoelastic experiments is given in detail.

In Part I the equation governing the reduction in energy transmission for given wave lengths and retardations is developed.

In Part II some influences are discussed which modify the final light distribution but which, either owing to the present lack of experimental data or for some other reason, have been neglected in the calculations.

In Part III a detailed color analysis is made of the fringes produced in models with stresses giving retardations up to 2μ.

© 1930 Optical Society of America

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Figures (7)

Fig. 1
Fig. 1

Schematical diagram of change in polarization of the light passing through a photoelastic instrument.

Fig. 2
Fig. 2

Energy distributions in the visible spectrum for black body radiations of 4800°K and 3000°K and for the latter radiation after transmission through the photoelastic apparatus in which is a model producing .7μ retardation.

Fig. 3
Fig. 3

Three sets of color mixture curves of the spectrum (spectral primaries .65μ, .53μ and .46μ) given by the three energy distributions shown in Figure 2.

Fig. 4
Fig. 4

Total luminosity of the transmitted light for increasing retardations.

Fig. 5
Fig. 5

Amounts of the spectral primaries (wavelengths .65μ, .53μ and .46μ) required to match the colors corresponding to given retardations.

Fig. 6
Fig. 6

(a) Energy distribution in the visible spectrum for a black body radiation of 3000°K. (b) Same radiation as (a) but after transmission through the photoelastic apparatus in which is a model producing 20μ retardation.

Fig. 7
Fig. 7

Color triangle using spectral primaries .65μ, .53μ and .46μ.

Tables (1)

Tables Icon

Table 1 Results of color analysis for increasing retardations

Equations (27)

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η 0 = a 0 cos ω t
x = a cos ω t = a sin ( ω t + π / 2 ) y = a cos ω t } .
a = a 0 / 2 .
x = a sin ω t y = a cos ω t } .
R = c ( p - q ) t
ϕ = R λ 2 π
x = a sin ω t y = a cos ( ω t - ϕ ) } .
x = a sin [ ( ω t - ϕ / 2 ) + ϕ / 2 ] = a cos ϕ / 2 sin ( ω t - ϕ / 2 ) + a sin ϕ / 2 cos ( ω t - ϕ / 2 ) y = a cos [ ( ω t - ϕ / 2 ) - ϕ / 2 ] = a cos ϕ / 2 cos ( ω t - ϕ / 2 ) + a sin ϕ / 2 sin ( ω t - ϕ / 2 ) } .
x = x 1 + x 2 y = y 1 + y 2 }
x 1 = a cos ϕ / 2 sin ( ω t - ϕ / 2 ) y 1 = a cos ϕ / 2 cos ( ω t - ϕ / 2 ) }
x 2 = a sin ϕ / 2 cos ( ω t - ϕ / 2 ) y 2 = a sin ϕ / 2 sin ( ω t - ϕ / 2 ) } .
x 1 = a cos ϕ / 2 sin ( ω t - ϕ / 2 ) y 1 = a cos ϕ / 2 cos ( ω t - ϕ / 2 - π / 2 ) = a cos ϕ / 2 sin ( ω t - ϕ / 2 ) }
x 2 = a sin ϕ / 2 cos ( ω t - ϕ / 2 ) y 2 = a sin ϕ / 2 sin ( ω t - ϕ / 2 - π / 2 ) = - a sin ϕ / 2 cos ( ω t - ϕ / 2 ) } .
η = a 0 cos ϕ / 2 sin ( ω t - ϕ / 2 ) .
ξ = a 0 sin ϕ / 2 cos ( ω t - ϕ / 2 ) .
ξ max = a 0 sin ϕ / 2.
E = E 0 sin 2 ϕ / 2
red 78.0             green 58.5             blue 30.0
C = .469 R + .351 G + .180 B .
ϕ 2 = R λ π = .7 .5 π
sin 2 ϕ 2 = .904.
red - .045             green .150             blue .090.
red - .041             green .136             blue .081
red 1.75             green 3.25             blue 2.8
C = .224 R + .417 G + .359 B .
L r = 38.5             L g = 100.0             L b = 3.72 ,
red 67             green 325             blue 10