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Figures (5)

F. 1
F. 1

Spectrophotometric test filters for color temperature determination. Transmission factors for blue filters, P, Q, R, T, U, W, X, Y and Z, and also neutral filters N1 to N4. Two or more letters on one curve indicate the curves of the separate filters are too nearly identical to be shown separated.

F. 2
F. 2

Interface reflection in a single filter. The light directly transmitted is indicated by the heavy line, while the lighter zig-zag line shows diagrammatically the reflection of energy between the two surfaces of the filter.

F. 3
F. 3

Twice reflected in a pair of filters. Each twice-reflected ray is analyzed in the tabulation into passages and additional passages.

F. 4
F. 4

This family of curves shows the temperatures attained with different groups of uniform filters. The spacing between curves is due to the difference in number, color and intensity of the interface reflections. The vertical distance between curves is due to interface reflection.

F. 5
F. 5

The ends of the broken curve show the color temperature of the standard lamp; the points next to the ends show the temperature given by the four neutral filters, while the five central points show how the temperature varies as the four neutrals are arranged in different orders with filter Y.

Tables (6)

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Table II Number of twice-reflected rays (t).

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Table III Passages of twice-reflected rays (r).

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Table IV Additional passages of twice-reflected rays (a).

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Table V Number of temperature combinations with eight different filters.

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Table VI Deviations from centering among test points. Test temperatures minus computed temperatures.

Equations (12)

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First filter 0 + 3 ( 2 p 1 ) 1 + ( p 1 ) ( 2 p 1 ) Second 1 3 + 3 ( 2 p 3 ) 3 + ( p 2 ) ( 2 p 3 ) Third 2 5 + 3 ( 2 p 5 ) 5 + ( p 3 ) ( 2 p 5 ) Fourth 3 7 + 3 ( 2 p 7 ) 7 + ( p 4 ) ( 2 p 7 ) p th ( p 1 ) ( 2 p 1 ) + 3 ( 2 p 1 ) 1 + 0
a = 4 p 3 2 [ p + 4 p ( p 1 ) + 4 3 p ( p 1 ) ( p 2 ) ] .
θ = θ 1 + θ 2 + θ p .
r = r 1 + r 2 + r p
a = a 1 + a 2 + a p .
A = 1 + s 2 [ r a p θ + 1 ( a 1 θ 1 + a 2 θ 2 + a p θ p ) ] 1 4
M = 1 + d T / T 0 d θ .
T θ = A θ 2 + [ ( p θ ) / ( p + θ ) ] 1 2 M A θ T 0 .
θ 1 = θ 2 = θ p = θ / p
A = 1 + s 2 [ r a p θ + 1 ( a 1 θ 1 + a 2 θ 2 + a p θ p ) ] 1 4 = 1 + s 2 [ r a p θ + 1 θ p ( a 1 + a 2 + a p ) ] 1 4 = 1 + s 2 [ r a θ θ + 1 a ] 1 4 = 1 + s 2 [ r θ θ + 1 ] 1 4 .
8 ! 2 S ( 8 p ) !
( T C ) n