# Inverse Square Law

Illuminance: The luminous flux falling into the normal unit area and normal to the direction of light is called illuminance. It is denoted by E.  Mathematically,

$$\text{E} = \frac{ \pi }{A} = \frac{4 \pi I}{A} = \frac{4 \pi I}{R^2} = \frac{I}{R^2}$$

Intensity of illumination: The amount of light energy incident on unit area of a surface per second is called intensity of illumination. It is also defined as the luminous flux falling normally per unit area of the surface held at that point. The unit of intensity of illumination is lux in SI unit and phot in CGS unit.

Let us consider a source of light placed at the centre of a hollow sphere of radius r. If Q is the amount of light energy emitted per second by the source and 4 πr2 is the area covered by the light energy. Then from definition, we can write:

$$I = \frac{Q}{A}$$

$$or, I = \frac{Q}{4 \pi r^2}…..(i)$$

Again from luminous intensity. we have:

$$L = \frac{Q}{4 \pi }$$

now, equation (i) becomes,

$$I \propto \frac{1}{r^2}$$

This shows that the intensity of illuminance of a source at a point is inversly propertional to the square of the distance from the source of light. This is called inverse square law.

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