The Concept of Luminous Flux
To understand photometry, we must first distinguish between physical energy and perceived light. Radiant flux is the total power emitted by a source in the form of electromagnetic radiation, measured in Watts (W). However, our eyes are not equally sensitive to all wavelengths; we are most sensitive to yellow-green light (approximately 555 nm). Luminous flux (denoted by Φ) is the measure of the perceived power of light, and its SI unit is the lumen (lm).
The relationship between radiant flux and luminous flux is defined by the luminous efficacy of radiation. A standard source emitting monochromatic light at 555 nm provides 683 lumens per watt. For other wavelengths, the luminous flux is scaled by the eye’s sensitivity curve, known as the photopic spectral luminous efficiency function. When solving problems, always remember that while energy is conserved in physics, “brightness” is a physiological perception tied to the spectral distribution of the source.
Luminous Intensity and Solid Angle
When light is emitted from a point source, it spreads out into space. To quantify how much light is emitted in a specific direction, we use luminous intensity (denoted by I). The SI unit for luminous intensity is the candela (cd), which is defined as one lumen per steradian (sr).
The solid angle (Ω) is the three-dimensional equivalent of a plane angle, measured in steradians. For a sphere, the total solid angle is 4π steradians. If a source emits light uniformly in all directions (an isotropic source), its total luminous flux Φ is related to its intensity I by the simple relation:
Φ = I × Ω = I × 4π
This formula is vital for exam calculations involving point sources. If the source is not isotropic, you must integrate the intensity over the solid angle to find the total flux.
Illuminance and the Inverse Square Law
Illuminance (denoted by E) measures the amount of luminous flux incident per unit area on a surface. Its SI unit is the lux (lx), where 1 lx = 1 lm/m². This is the quantity most relevant to practical lighting design and experimental physics problems involving light meters.
The Inverse Square Law describes how illuminance changes with distance from a point source. If a source of intensity I illuminates a surface at a distance r, and the light rays strike the surface normally (perpendicularly), the illuminance is given by:
- E = I / r²
If the surface is tilted such that the light rays make an angle θ with the normal to the surface, the effective area increases, and the illuminance follows the Lambert’s Cosine Law: E = (I / r²) cos θ. This is a classic trap in competitive exams; always check the orientation of the surface relative to the incident light beam.
Important Facts and Formulas
| Quantity | Symbol | SI Unit | Definition/Formula |
|---|---|---|---|
| Luminous Flux | Φ | Lumen (lm) | Perceived power of light |
| Luminous Intensity | I | Candela (cd) | Flux per unit solid angle (lm/sr) |
| Illuminance | E | Lux (lx) | Flux per unit area (lm/m²) |
| Inverse Square Law | – | – | E = I / r² (for normal incidence) |
Applications and Exam Strategy
In IIT JEE and similar competitive exams, photometry questions often combine geometry with physics. You might be asked to calculate the illuminance on a desk at a specific distance from a lamp, or the total flux received by a screen placed at an angle. The most common mistake is failing to account for the cos θ term when the surface is not perpendicular to the rays.
Always visualize the solid angle. If a problem describes a light source inside a sphere or a cone, identify the solid angle subtended by the surface. Remember that intensity (I) is a property of the source, whereas illuminance (E) is a property of the surface being illuminated. Never confuse the two.
Key Points to Remember
- The human eye is most sensitive to light at 555 nm.
- 1 candela is the intensity of a source emitting 1 lumen per steradian.
- Total flux from an isotropic source is 4πI.
- Illuminance decreases with the square of the distance (1/r²).
- Lambert’s Cosine Law (E = I cos θ / r²) is essential for tilted surfaces.
- Always check units; ensure distances are in meters and areas are in square meters.
Quick Revision Summary
- Photometry evaluates light based on human visual perception.
- Luminous Flux (Φ): Total light power emitted, measured in lumens.
- Luminous Intensity (I): Light emitted per solid angle, measured in candelas.
- Solid Angle (Ω): 3D angle measured in steradians; full sphere = 4π sr.
- Illuminance (E): Light incident per unit area, measured in lux.
- Inverse Square Law: E ∝ 1/r² applies to point sources.
- Cosine Law: E ∝ cos θ accounts for the angle of incidence.
- Units: 1 lux = 1 lumen / m².
