# intensity of beam of light

• April 9th 2010, 07:22 PM
sigma1
intensity of beam of light
i have a tricky question here, i hope am putting it in the correct section.

the intensity (I) of a beam of light after passing through a material is given by the formula ( i did it as an attachment so look at it please)

where k is the initial intensity
T is the thickness of the material in cm
c is the absorbtion constant
if the value of c = 0.0101, at what depth will a vertical beam of light be reduced to 50% of its initial intensity.
• April 9th 2010, 08:06 PM
sa-ri-ga-ma
At the depth T, intensity I = k/2.
So k/2 = 4^-cT*k
2 = 4^cT
ln(2) = cT*ln(4)
Now solve for T.
• April 9th 2010, 08:21 PM
macosxnerd101
This is more of a question of what value of T will make $1/4^{cT}$ will generate 1/2. Or in other words, what value of T we need to cut 4 in half. Since $4^{cT}$ is equivelant to $(4^c)^T$, we can set up a log equation.

So since $(4^c)^T = 2$, then $log_{4^c}(2) = T$
• April 9th 2010, 08:51 PM
sigma1
i think i know it would come to a log but am afraid am a bit confused on solving it. and which one of the approach am i suposed to take?
• April 9th 2010, 09:00 PM
macosxnerd101
Try them both and see which you prefer. My approach is from the definition of a logarithm. That is:
$
x = b^y
\log_b(x) = y
$

The approach sa-ri-ga-ma took is basically the same thing with a change of base formula thrown in.