Illuminance and distance from the source
Study of the inverse square law for illuminance with a smartphone
Author:
Title 4
Learning objectives :
This activity allows students to experimentally verify the inverse square law that governs the propagation of light. It develops the ability to make systematic measurements and identify mathematical relationships.
Concepts covered
Inverse square law; Bright illuminance; Light propagation; Mathematical modeling; Data interpolation
What students will do :
The student uses the brightness sensor of an Android smartphone and the FizziQ application to measure illuminance at different distances from a point light source. By taking measurements at regular intervals and organizing the data in a table, the student can draw an illumination curve as a function of distance and then determine the mathematical relationship that models this propagation.
What is required :
Android smartphone with FizziQ app and light sensor; A lamp without a shade as a point light source; A room that can be darkened; A tape measure; FizziQ experience notebook
Scientific background :
The inverse square law is a fundamental physical principle that describes how the intensity of a phenomenon decreases with distance from its source. For light, the illuminance E (measured in lux) is inversely proportional to the square of the distance r from the source: E = I/(4πr²), where I is the light intensity of the source. This relationship is explained by the dispersion of light energy on increasingly large spherical surfaces as we move away from the source. On a graph, this relationship is manifested by a hyperbolic curve of type y = k/x². The light meter built into some Android smartphones uses a photocell that converts light into an electrical signal. Its precision, although lower than that of a professional light meter, is sufficient to verify the inverse square law. Some experimental difficulties can affect measurements: the source is never perfectly point-like, reflections off walls can add stray light, and the exact position of the sensor in the smartphone can be difficult to determine. The FizziQ interpolation tool allows you to confirm the relationship in 1/r² and estimate the proportionality coefficient. This same law applies to other phenomena such as sound and gravitational or electric fields, illustrating the universality of certain physical principles.