Page 161 - Offshore Electrical Engineering Manual

148 CHAPTER 14 Offshore Lighting

FIGURE 2.14.3
Illumination effect of a linear source of light.

Consider an element δx at S, distant x from A. ST lies in the axial plane and is
normal to the axis of the source. Let I(α,θ) be the intensity of the source AB in the
direction parallel to SP. The illuminance δE at P on the plane CD due to element δx
of the source is then given by:
δxI (α , θ) cos α cos φ
δE = · 2 .
l (ϰ/sinα) (2.14.2)
h x
Since AP = =
cosθ tanα
and x = h tan α sec θ
2
δx = h sec α sec θ δα
Substitution of these for x and δx in Eq. (2.14.2) gives

I (α , θ)
δE = cos θ cos ϕ cos α δα
lh
For the whole length of the source,

I (0 , θ) β I (α , θ)
E = cos θ cos ϕ∫ 0 cos α dα
1h I (0 , θ) (2.14.3)