each 1.0 mm of a filter through which light passes reduces the intensity of the light by 12%.How thick should be to reduce the intensity of the light to 20%?
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each 1.0 mm of a filter through which light passes reduces the intensity of the light by 12%.How thick should be to reduce the intensity of the light to 20%?
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Verified answer
This is a geometric series problem.Let E be intensity of light just before entering the filter.
Each 1 mm of filter reduces intensity of light by 12% => intensity becomes 88%.
From 0mm to 1mm intensity becomes : 88% or 0.88 * E
from 1 mm to 2 mm 0.88 * 0.88 * E = 0.88² E
from 2 mm to 3 mm = 0.88³ E
At x mm thickness intensity becomes = 0.88^x E
finally we want 0.88^x E = 20% E = 0.20 E
So 0.88^x = 0.20
take logarithms on both sides,
x log 0.88 = log 0.20
x = log 0.20 / log 0.88 = 12.59 mm