Recitation Exercise #3, Physics 142, 9-5-00
Name Example Solution _______________________
Last four digits of student number 1096 _____________
You can earn up to 15 points based on your work.
This exercise is open-book / open-notes, but not open-neighbor.
Create 2 2-digit numbers from the last four digits of your student number.
a) first two digits: _____10______
b) last two digits: _____96______
a) If you have a filter (number a mm) _____10 mm_ thick, which transmits 10% of the
incoming light intensity, how thick must a filter of the same material be to transmit
(number b percent) _____96%______ of the incoming light intensity?
This has to do with transmittance through filters, so we will use
Bouguer's law:
I = I0e-t
(Note:
It would work just as well to use Bouguer's
law as an exponent in base 10 … I = I010-kt … that would change
every "ln" below to "log", but the equation manipulation would be
otherwise unchanged.)
We can use the information
absorption coefficient ()
filter thickness needed to
First, find the absorption
about the first filter to find the
for this material, and then find the
produce the desired percent transmittance.
coefficient:
10% = (100%)e-(10 mm)
0.1 = e-(10 mm)
ln(0.1) = ln (e-(10 mm)) = -(10 mm)
 = -ln(0.1)/(10 mm) = 0.23 mm-1
(Note: The absorption coefficient has the units necessary to make
the total exponent, t, unitless!!)
Now use this to find the necessary filter thickness:
0.96 = e-t = e-(0.23/mm)t
ln(0.96) = ln(e-(0.23/mm)t) = -(0.23 mm-1)t
t = -ln(0.96)/(0.23 mm-1) = 0.18 mm