Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Relation among Illumination, Brightness, and Luminous Intensity
Illumination
The luminous flux received by the surface per unit area is known as illumination. It is denoted by the letter 'E' and is measured in Lux or Lumen/m2.
Mathematically, the illumination is given by the expression,
$$\mathrm{Illumination,\mathit{E}\: =\: \frac{Luminous \: Flux\left ( \phi \right )}{Area \left (\mathit{A} \right )}\: =\:\frac{\mathit{C\, P}\times \omega }{\mathit{A}}}$$
Luminous Intensity
Luminous intensity is defined as the amount of luminous flux emitted into a solid angle of a space in a specified direction. It is denoted by 'I' and is measured in Candela.
Mathematically,
$$\mathrm{Luminous\:Intensity,\mathit{I}\: =\: \frac{Luminous \: Flux}{Solid \: angle}}$$
Brightness
The luminous intensity per unit surface area of the projected surface in the given direction is known as brightness of that surface. It is denoted by 'L' and is given by,
$$\mathrm{Brightness,\mathit{L}\: =\: \frac{Luminous \: Intensity\left ( \mathit{I} \right )}{Projected\: Area}\: =\:\frac{\mathit{I}}{\mathit{A}\, cos\, \theta }}$$
Relation among Illumination, Luminous Intensity and Brightness
Consider a sphere with radius 'r' meters, having a source of 1 candle power and luminous intensity of 'I' candela at its center. Then, from the definitions, we have,
$$\mathrm{Brightness,\mathit{L}\: =\:\frac{\mathit{I}}{\pi \mathit{ r^{\mathrm{2}}}}\: \: \: \cdot \cdot \cdot \left ( 1 \right )}$$
And,
$$\mathrm{Illumination,\mathit{E}\: =\:\frac{\phi }{\mathit{A}}\: =\:\frac{C\, P\times \omega }{\mathit{A}}}$$
For a sphere,
$$\mathrm{\mathit{A}\: =\:4\pi \mathit{r}^{2}\: \: and\: \: \omega \: =\:4\pi }$$
$$\mathrm{\mathit{\therefore E}\: =\:\frac{\mathit{I}\times 4\pi }{4\pi \mathit{r}^{2}}\: =\:\frac{\mathit{I}}{\mathit{r}^{2}}\: \: \: \cdot \cdot \cdot \left ( 2 \right )}$$
From equations (1) & (2), we get,
$$\mathrm{\mathit{E}\: =\:\pi \mathit{L}\: =\:\frac{\mathit{I}}{\mathit{r}^{2}}\: \: \: \cdot \cdot \cdot \left ( 3 \right )}$$
Equation (3) gives the relation among luminous intensity (I), illumination (E) and brightness (L).
2K+ Views
