Page 80 - Engineering Plastics Handbook

54 Introduction

Fresnel’s equation is used to estimate the amount of light reflected
under ideal conditions [9].
n cosθ − n cos θ
R = 2 1 1
f n cosθ + θ
2 1 n cos
1
where R = amount of light reflected
f
n = refractive index of one medium
2
θ = angle of refraction, rad (deg)
1
n = refractive index of other medium
1
θ=θ incidence =θ reflection , rad (deg)
As light travels through a clear plastic, imperfections and impurities
greatly diminish light intensity, which scatters and attenuates expo-
nentially by light absorption. The amount that light intensity diminishes
can be estimated by
−µx
I = I e
0
x
where I = intensity of light beam at x, cd (fc), lx
x
I = free air density
0
µ= plastics attenuation coefficient at x
x = distance light traveled through plastics at I , cm (in)
x
1 candela (cd) = 10.74 lux (lx)
Measure with a lightmeter.
The total attenuation coefficient α is used to calculate the amount of
t
light lost when light is transmitted through a plastic light pipe, assum-
ing no light is lost by refraction from the critical angle. Coefficient α is
t
the sum of (1) refraction at entrance and exit (of plastic light pipe), (2)
material absorption per unit length of light pipe, (3) loss at each reflec-
tion, and (4) number of reflections per unit length [9].
Surface imperfections and impurities scatter light which reflects off
the interface of the plastic and air (or other medium). The amount of
light scattered at each reflection is estimated as loss per reflection.
Light loss by reflection is calculated as [9]
 cos  2
θ
Λ = e πσ r 2 

reflection
 λ n 
= light loss per reflection
where Λ reflection
σ= surface roughness, mm (in); height from surface of sur-
face imperfections, measured from the mean
r = thickness of plastics, cm (in)
θ= angle of incidence of light rays entering plastics surface
from air (medium), rad (deg)
λ = wavelength of light source in plastics
n