Question

Measurement of optical absorption of a solution is disturbed by the additional stray light falling at the photo-detector. For estimation of the error caused by stray light the following data could be obtained from controlled experiments.
• Photo-detector output without solution and without stray light is 500 µW.
• Photo-detector output without solution and with stray light is 600 µW
• Photo-detector output with solution and with stray light is 200 µW

The percent error in computing absorption coefficient due to stray light is

• A. 31.66
• B. 12.50
• C. 33.33
• D. 94.98

Answer 1

The correct option is A 31.66

Case-I (Measure value)
$I_0=600\mu W$
I(t) = $600\mu W$
I(t) = $I_0{e}^{-\mu }M{V}^x$
${\mu }_{MV}=-ln\left(\frac{2}{6}\right)=-ln\left(0.33\right)$

Case-II (True value)
$I_0=500\mu W$
$I\left(t\right)=100\mu W$
I(t) = $10e^{-\mu }T{V}^x$

${\mu }_{TV}=-ln\left(\frac{1}{5}\right)=-ln\left(0.2\right)$



$=\frac{[-ln(0.33\left)\right]-[-ln(0.2\left)\right]\times 100}{-ln\left(0.2\right)}$

= 31.7%