Irradiance is the power per unit area incident on a surface.

The following relationship links irradiance, the power of radiation incident on a surface and the area of the surface, and can be used to solve problems involving these quantities.

$$ I=\dfrac{P}{A} $$

→ The unit of irradiance is $Wm^{-2}$

Irradiance is inversely proportional to the square of the distance from a point source.

This law is only true for a point source. A point source of light emits light in all directions, covering a spherical area, e.g. a light bulb. A laser is not a point source of light because it only spreads its light over a very small area in a directed beam.

→ So at a distance of $2m$, for example, a point source of light could cast its light over an area of a sphere with radius $2$.

→ This means that if the distance from a point source is doubled, then the then the irradiance will be quartered.

The following relationships link irradiance and distance from a point source of light, and can be used to solve problems involving those quantities.

$$ I=\dfrac{k}{d^2} $$

$$ I_1d_1^2=I_2d_2^2 $$

The following is the experiment to verify the inverse square law for a point source of light.

Apparatus

• dark room
• metre stick
• $12V$ lamp
• light sensor and meter

Method

1. Connect the lamp to a suitable power supply and ensure that it lights up. The voltage to the lamp must be kept constant throughout the experiment.
2. Position the light sensor at $0.1m$ away, measured with the metre stick, from the lamp and measure the irradiance.
3. Repeat the irradiance measurements for different distances away from the lamp, using a metre stick to measure the distance.