Laws of Illumination

Light is an essential element in human life and the day-to-day activities of human beings eventually depend on the light. Where there is no natural light, the use of artificial light is required. Artificial lighting is generated electrically, because of its cleanliness, ease of control, accuracy, and stable output, as well as its low cost it is taking an increasingly major part in modern everyday life.

The science of illumination engineering has become of major importance. Light is a form of luminous energy. Several forms of incandescent bodies are the reference of light and the light radiated by such bodies depends upon the temperature of bodies. Heat energy is emitted into the medium by a body that is much warmer than the medium surrounding it. The heat of the body can be categorized as red-hot or white-hot.

What is Illumination?

Illumination is denoted by ‘E’. Illumination is defined as the luminous flux obtained by the surface per unit area. Luminous flux is the total amount of light energy emitted per second from a luminous body. Illumination varies from light, however these terms are used more or less the same. Light originates from a source, and illumination results from its interaction with surfaces upon which it falls. This illumination alters the surface appearance, making it appear brighter or darker with particular colors.

However, the brightness and color perceived by the eye may sometimes interfere with what is considered useful or acceptable. Light may be created by flowing an electric current through filaments like in incandescent lights, through arcs between metal rods or carbon rods, or appropriate gases like neon and other gas tubes.

In several lamps, the light is due to fluorescence elevated by radiation emerging from the moving of electric current through mercury vapor. Some bodies reflect light at some rate, and when illuminated from the primary source they become secondary sources of light. A good example is the moon, which illuminates Earth through the reflected light emerging from the sun.

Illumination is measured in lux or lumen/m².

Illumination Important Terms

• Light: It is the part of radiant energy from a hot body which produced the visual sensation on human eye.
• Luminious flux: The total quantity of radiant energy per second accountable for visual impact from a luminous body is called Luminious flux.
• Lumen: It is the unit of luminous flux. One lumen is defined as the ratio of luminous flux emitted to unit solid angle from a point source of one candle power.
• Solid angle: Solid angle is defined as the angle subtended by the partial surface area of a sphere at its center.
• Candle power: The light emitting capacity of a source is called its candle power.
• Luminous intensity: It is the luminous flux emitted by the source per unit solid angle in that direction.
• Reduction factor: It is a source of light is the ratio of its mean spherical candle power to its mean horizontal candle power.
• Lux: One meter candle or lux is defined as the illumination produced by a uniform source of one Candle Power on the inner surface of a sphere of radius one meter.

Properties of Illumination

The properties of illumination are:

• Uniformity: Stability illumination makes the light is evenly distributed that improves the performance.
• Glare: Glare appears when there is extreme contrast in brightness within the field of view that cause difficulty or discomfort in seeing. Using the proper lighting design glare can be minimized.
• Energy: It makes easy way to save energy as illumination is flexible to changing conditions according to the light.
• Direction: Illumination can be either directional or diffuse. Directional means light in specific direction and diffuse means light can be spread evenly in all directions.
• Flickering: Illumination does not cause any discomfort like flickering or over lighting. Flickering means change in the intensity of light that cause discomfort for human eyes.

Laws of Illumination

The two laws of illumination are:

• Inverse Square Law or The Inverse Square Law of Illuminance
• Lambert’s Cosine Law or The Cosine Law of Illuminance

The Inverse Square Law of Illuminance

Inverse square law means ‘It is the illumination of a surface that is inversely proportional to the square of distance between the surface and light source’.

Consider the figure below,

Inverse square law

The Cosine Law of Illuminance

Lambert’s cosine law means ‘illumination at any point on a surface is directly proportional to the cosine of the angle between the normal at that point and the line of flux’.

Lambert’s cosine law

Assume the surface is inclined at an angle ‘θ’ to the line of flux as shown above,

Let AB be the surface area normal to the source and inclined at ‘θ’ to the vertical axis.

CD be the surface area normal to the vertical axis and inclined at an angle ‘θ’ to the source ‘O’.

From the figure,

[Tex]AB= CD \cos \theta[/Tex]

For the area A1 ,

Solid angle is,

[Tex]\omega = \frac{\text{area of AB}}{d^{2}}[/Tex]

we know that,

flux = luminous Intensity x Solid angle

[Tex]\text{flux}=I \times \omega[/Tex]

[Tex]\text{flux}=I\times \frac{\text{area of AB}}{d^{2}}[/Tex]

Let the Illumination be E₁ on Area of AB,

[Tex]\text{Illumination} = \frac{\text{flux}}{\text{area}}[/Tex]

[Tex]E_{1}=I\times \frac{\text{area of AB}}{d^{2}}\times\frac{1}{\text{area of AB}}[/Tex]

[Tex]E_{1}= \frac{I}{d^{2}}[/Tex]

Similarly,

Illumination be E₂ on Area of CD,

[Tex]\text{Illumination} = \frac{\text{flux}}{\text{area of CD}}[/Tex]

[Tex]E_{2}=I\times \frac{\text{area of AB}}{d^{2}}\times\frac{1}{\text{area of CD}}[/Tex]

[Tex]\text{area of CD}=\frac{\text{area of AB}}{\cos \theta}[/Tex]

[Tex]E_{2}=I\times \frac{\text{area of AB}}{d^{2}}\times\frac{1}{\frac{\text{area of AB}}{\cos \theta}}[/Tex]

[Tex]E_{2}=\frac{I}{d^{2}}\cos \theta[/Tex]

From the figure,

[Tex]\cos \theta =\frac{h}{d}[/Tex]

[Tex]d = \frac{h}{ \cos \theta}[/Tex]

where d= distance, h= height

Substitute d value in E₂ ,

[Tex]E_{2}=\frac{I}{(\frac{h}{\cos \theta})^{2}}\cos \theta[/Tex]

[Tex]E_{2}=\frac{I\cos^{2} \theta}{h^{2}}\cos \theta[/Tex]

[Tex]E_{2}=\frac{I}{h^{2}}\cos^{3} \theta[/Tex]

Theory of Light

The Sensitivity of the human eye is specific across colors in range of wavelengths from 0.004 mm to 0.00075 mm (equivalent to 4,000 to 7,500 Angstrom Units). Within this spectrum eye perceives different wavelengths as distinct colors.

Theory of Light

The range of electromagnetic radiation visible to the human eye is quite less Which Spans from approximately 4.3×10

¹⁴

Hz to 7.5×10

¹⁴

Hz. The White sunlight consists of various colors which falls within this visible spectrum with wavelengths ranging from 4,000 to 7,500 Angstrom Units (AU).

Classic Lighting Techniques

The Classic Lighting Techniques refer to established methods of illuminating in subject with photography, cinematography, and other visual arts. These Techniques have been refined with time and are often based on principles of balance, contrast, and aesthetics. It Aims to create visually appealing and impactful images by controlling the distribution and quality of light. Examples of the classic lighting techniques are Three-point lighting, Rembrandt lighting, butterfly lighting, split lighting, chiaroscuro lighting, and silhouette lighting.

Solved Examples on Laws of Illumination

A surface is inclined at an angle 30° to the rays is kept 3 m away from 120 candle power lamp. Find the average intensity of illumination on the surface.

Consider the figure from the data as shown below,

Solved Example

From the figure,

𝝷 = 90°- 30°= 60°

Average illumination is,

[Tex]E=\frac{I}{d^{2}}\cos \theta[/Tex]

[Tex]E=\frac{120}{3^{2}}\cos 60^{\circ}[/Tex]

E = 6.66 lux

The illumination at a point on a working plane below the lamp is to be 50 lumens/m². The lamp gives 110 candle power uniformly below the horizontal plane. Find: (a). The height at which lamp is suspended. (b). The illumination at a point on the working plane 3 m away from the vertical axis of the lamp.

Given data,

Candle power of the lamp = I = 110 CP.

The illumination IS E = 50 lumen/m².

Example 2

(a). From the Figure, the illumination just below the lamp, i.e., at point B:

[Tex]E_{B}=\frac{I}{h^{2}}[/Tex]

[Tex]h= \sqrt{\frac{I}{E_{B}}}[/Tex]

[Tex]h= \sqrt{\frac{110}{50}} [/Tex]

h= 1.48 m

(b) Illumination at point A is,

[Tex]E_{A}=\frac{I}{h^{2}}\cos^{3}\theta[/Tex]

[Tex]E_{A}=\frac{110}{3^2} \times (\frac{3}{\sqrt{3^{2}+1.48^{2}}})^{3}[/Tex]

E_A = 8.8 lux

Advantages of Laws of Illumination

• Energy efficient lightening solution. Energy can be minimized using the illumination levels.
• laws of illumination provides flexibility, So these are useful to provide unique lighting designs.
• Applying Laws of illumination laws can elevate the photographs, spaces or designs.
• Stick to the illumination laws, then it can improve lighting for functionality and efficiency. Proper illumination can improve visibility, reduce glare and shadows.
• For the different situations laws of illumination gives compatible suggestion for getting the required lighting effects.

Disadvantages of Laws of Illumination

• Proper maintenance is required to get better performance.
• Lighting perceptions are personal and will be different from one another that will effect the consideration of lighting environments.
• Fixing with the laws of illumination can increase the cost.
• Some laws of illumination can be complex.
• Using illumination laws provides energy efficiency and some lighting solutions can cause light pollution.

Applications of Laws of Illumination

• Laws of illumination is used in astronomy, to calculate the brightness of the star.
• Used in design, engineering and architecture.
• Inverse square law is used in photography to find the variation in illumination on an area as it is moving closer or away from the Light source.
• Illumination laws are used in medical Imaging.
• Used in navigation and aviation for safe landing, take -off and in low brightness situations.

Conclusion

The laws of illumination plays a major in different application from astronomy to aviation and in architecture. Laws of illumination advantages like energy efficiency, flexibility are used in different applications like design, medical, aviation and astronomy apart from the disadvantages like inverse square law measure the illuminance on horizontal surfaces, lambert’s square law measure illuminance on inclined surfaces. Then, the interpretation and application of illumination laws are necessary for technology advancement, Better quality of life, and Enhancing the human exposure to different domains.

Laws of Illumination – FAQs

What is the unit of illuminance or Illumination ?

The unit of illuminance is Lumen per square meter (Lumen/ m² ) (or) lux (or) meter – candle.

What is meant by Luminous flux ?

It is defined as the total quantity of radiant energy per second accountable for visual impact from a luminous body. It is denoted by Φ. SI unit of Luminous flux is ‘lumen’.

What is meant by Solid angle ?

It is the ratio of area of the surface to the square of radius of sphere. Solid angle is also defined as the angle subtended by the partial surface area of a sphere at its center. Solid angle is denoted by 𝛚. It is measured in ‘steradians’.