Question

Derive the relation between coefficient of absorption, coefficient of reflection and coefficient of transmission.

Answer 1

Let Q represent the amount of radiant energy incident on a body, and let Q_a, Q_r, and Q_t represent the amounts of radiant energy the body simultaneously absorbs, reflects, and transmits. Since there is a conservation of energy overall, we have,

Q_a + Q_r +  Q_t = Q

∴ `Q_a/Q + Q_r/Q + Q_t/Q` = 1

We know that,

`Q_a/Q = a`    ...(By definition of coefficient of absorption)

`Q_r/Q = r`    ...(By definition of coefficient of reflection)

`Q_t/Q = t`    ...(By definition of coefficient of transmission)

Hence, a + r + t = 1

This is the required relation.