The Cosine Law of Illuminance is fundamental principle in lighting design and engineering that describes the relationship between the angle of incidence of light and the level of illuminance on a surface.
The law states that the illuminance on a surface is proportional to the cosine of the angle of incidence of the light on the surface.
Illuminance at a point on a plane is proportional to the cosine of the angle of light incident (the angle between the direction of the incident light and the normal to the plane).
Eθ = E cosθ
Where E is the illuminance on the surface in lux (lx), E0 is the illuminance on a surface that is perpendicular to the incident light, and θ is the angle of incidence between the light and the surface.
This means that as the angle of incidence between the light and the surface increases, the illuminance on the surface decreases. At an angle of 90 degrees, the cosine of the angle is zero, and the illuminance on the surface is also zero.
The Cosine Law of Illuminance is important to consider when designing lighting systems, as it can have a significant impact on the level of illumination achieved in a space, particularly in applications where light is directed at an angle to the surface, such as in outdoor lighting or in the lighting of artwork or displays.
It should be noted that the Cosine Law of Illuminance assumes that the surface being illuminated is flat and perpendicular to the incident light, and for surfaces that are not flat or perpendicular, other factors may need to be taken into account.
Let us assume that the surface is inclined at an angle ‘θ’ to the lines of flux as shown
in Fig. (a)
PQ = The surface area normal to the source and inclined at ‘θ’ to the vertical axis.
RS = The surface area normal to the vertical axis and inclined at an angle θ to the source ‘O’.
From Fig (b)
cosθ = h/d
or d = h/cosθ
Substitute value of d in above equation
where d is the distance between the source and the surface in m, h is the height of source from the surface in m, and I is the luminous intensity in candela.
Hence, above Equation is also known as ‘cosine cube’ law. This law states that the illumination at any point on a surface is dependent on the cube of cosine of the angle between line of flux and normal at that point.
Note – From the above laws of illumination, it is to be noted that inverse square law is only applicable for the surfaces if the surface is normal to the line of flux. And Lambert’s cosine law is applicable for the surfaces if the surface is inclined an angle ‘θ’ to the line of flux.
The Inverse Square Law of Illuminance
Laws of Reflection and Refraction
Illumination in architecture – home page
FD Architect Community Forum Discussion
- Illumination – introduction
- Basic Terminology and Definitions
- Laws of Illumination The Inverse Square Law of Illuminance Illuminance (E) at any poi
- Laws of Reflection and Refraction
- Visual efficiency & comfort
- Day lighting
- Components of Daylight Factor
- Artificial Lighting Design
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