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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