Intensity Formulas - Definitions & Solved Example Questions

Intensity is a measure of the energy transmitted by a wave. It is the quantity of energy the wave –conveys per unit time over unit area. It is generally measured with units of watts per square metre (i.e., Wm–2). Intensity will depend on the strength and amplitude of a wave. Intensity is represented by \[I\]. The formula for intensity is given by,

\[I = \frac{P}{A}\]

Where \[I\] is the intensity, P is the power and A is the area of cross section.

Example: What is the intensity of light incident normal to a circular surface of radius 5 cm from a 100 W source of light?

Solution:

r = 5 cm = 5 × 10–2 m, P = 100 W, \[I\]=?

\[I = \frac{P}{{\pi {r^2}}} = \frac{{100}}{{\pi \times {{(5 \times {{10}^{--2}})}^2}}} = 1.27 \times {10^4}W{m^{--2}}\]

Question: The intensity of a light source with power P on a circular surface of radius r placed at a certain distance is \[I\]. If at the same distance from another source, if the intensity on a circular surface of double the radius, is 4\[I\], then what is the power of the second source?

Options:

(a) 4 P

(b) 16 P

(d) P / 4

Answer: (b)