intensity of light log question

Question

The intensity, I, of light, in lumens, passing through the glass of a pair of sunglasses is given by the equation I(x)= I∨0 (0.8)^x, where x is the thickness of the glass, in millimetres, and I∨0 is the intensity of light entering the glasses. How thick should the glass be so that it will block 25% of the light entering the sunglasses?

 

How to get 1.3mm

 

Answer 1

I(x) = I₀(0.8)^x

 

I(x) is the amount that gets through.  If the glass blocks 25% of the light, then 75% of the incoming intensity gets through.

 

0.75I₀ = I₀(0.8)^x

 

0.75 = 0.8^x

 

 

Taking the logarithm of both sides,

 

ln(0.75) = ln(0.8^x)

 

ln(0.75) = x ln(0.8)     [power rule for logarithms]

 

x = ln(0.75) / ln(0.8) = 1.29 mm