Laws of Illumination including Inverse Square Law

Before discussing the laws of illumination, we would recall the term illumination. Illumination is defined as the incident luminous flux per unit area on a surface. Luminous flux is the radiation of light energy per second. If certain luminous flux F falls on a surface area A square meter then the illumination will be F/A.

There is another important term related to light energy. This term is luminous intensity. Let us imagine a light source emits light of luminous flux F through a solid angle ω. Then the luminous intensity of the light will be F/ω. In other words we can say luminous intensity is the luminous flux created by a light source per unit solid angle.

Laws of Illumination

First law of illumination

Consider a sphere of radius r. Let us take an area A on the surface of the sphere. This area creates a solid angle ω with the center of the sphere.
first law of illumination
Now we can write

Here, r is constant so we can write

Now, multiplying both sides with luminous flux F we get,

So, illumination is directly proportional to the luminous intensity of a light source.

Second Law of Illumination

We known second law of illumination as Inverse Square Law also. This law says the illumination at any point is inversely proportional to the square of the distance from the center of the light source. One can derive the expression of this law from the expression of illumination itself.

This implies,

If we go away from the center of the light source, the surface area created by a certain solid angle will also increase accordingly. And this increment is proportional to the square of the perpendicular distance of the area from the center of the light source.

This solid angle confines a fixed amount of luminous flux. Let us say it is F. If the area on which this luminous flux incident, increases then the flux per unit area decreases accordingly.

Third Law of Illumination

If the luminous flux does not strike on a surface area perpendicularly, then the illumination is directly proportional to the cosine of the angle of alignment of the surface. The angle of alignment means the angle made by the surface to the plane perpendicular to the incident luminous flux. Let us explain this law of illumination in brief. We are having a plane of area A. The angle between this plane and the imaginary plane perpendicular to the incident flux is θ.
Third Law of Illumination

Hence, only Acosθ area will be projected perpendicularly in front of the incident luminous flux. So from the above-drawn figure, we can see that only Fcosθ portion of the incident flux will now strike on the entire area A of the plane. At that condition the expression of illumination is

Hence, we can write,

Now by combining these all three laws of illumination, we can write

So, at last, we can brief the laws as

  1. Illumination on an illuminated plane is directly proportional to the luminous intensity of a light source.
  2. This is inversely proportional to the square of the perpendicular distance of the plane from the center of the light source.
  3. The same is also directly proportional to the cosine of the angle made by that plane with the imaginary plane perpendicular to the direction of luminous flux.

 

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