The intensity of a narrow beam of monochromatic light passing through a homogeneous…

PHYSICS · Subjective · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

The intensity

I

of a narrow beam of monochromatic light passing through a homogeneous medium falls exponentially with the distance

x

travelled according to

I = I_{0}e^{-\mu x},

where

I_{0}

is the initial intensity and

\mu

is the absorption coefficient of the medium. (i) Show that the exponent

\mu x

must be dimensionless. (ii) Hence obtain the dimensions and SI unit of the absorption coefficient

\mu

. (iii) A glass sample has

\mu = 0.15\,\text{cm}^{-1}

. Convert this value to its numerical magnitude in SI units.