3M BEF film is placed over the backlights that provide the light to illuminate L

Question

3M BEF film is placed over the backlights that provide the light to illuminate LCD screens used in televisions, monitors, tablets and cell phones). By using two sheets, the light can be directed into a cone where it is more directed towards the user of the product, with the most light coming out normal to the surface and a half-brightness of about 30 degrees from the surface. If theta is the angle from normal of the surface and the luminous intensity follows the following graph, calculate the percentage of light that is within the cone from 0 to 10 degree, 0 to 20 degree and 0 to 30 degree.

Explanation / Answer

From the graph, equation of the line is
y = mx + c
at y = 0, x = 60 deg
at y = Imax, x = 0

so, Imax = c
60m + Imax = 0
m = -Imax/60

so y = -Imax*x/60 + Imac = Imax(1 - x/60)

percent intensity, Ip = y*100/Imax = 100 - 5x/3 [ x in degrees]

so weighted average percentage of light between x2 and x1 is
I' = integrate (Ipdx)/integrate (x)
I' = integrate(100 - 5x/3 )dx / intefrate (dx)
I' = (100(x2 - x1) - 5(x2^2 - x1^2)/6)/(x2 - x1)

so, for x2 = 10, x1 = 0
I' = (100(10 - 0) - 5(100 - 0)/6)/(10 - 0) = 91.66 percent

so, for x2 = 20, x1 = 0
I' = (100(20 - 0) - 5(400 - 0)/6)/(20 - 0) = 83.33 percent

so, for x2 = 30, x1 = 0
I' = (100(30 - 0) - 5(900 - 0)/6)/(30 - 0) = 75 percent

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