Overview

This project focused on experimentally measuring light intensity using an Arduino-based sensing platform to validate two fundamental radiative principles: the inverse-square law and Lambert’s cosine law. The system combined hardware interfacing, data acquisition, and numerical analysis to compare theoretical predictions against measured results under controlled conditions.

Experimental Setup

An Arduino Uno was configured with a light-dependent resistor (LDR) in a voltage-divider circuit to measure illumination in analog-to-digital converter (ADC) units. The sensor output voltage varied with incident light intensity and was sampled through the Arduino’s A0 analog input.

Two experimental configurations were conducted:

Intensity vs. Distance: Measurements taken from 1 ft to 20 ft with the sensor oriented normal to the light source.
Intensity vs. Angle: Measurements collected from −90° to +90° at a fixed distance to study angular dependence.

Data was streamed over serial communication and post-processed in MATLAB.

Data Analysis & Modeling

Measured light-intensity data was fit against the following theoretical models:

Inverse-Square Law \(I(r) = \frac{a}{r^2}\)

Lambert’s Cosine Law \(I(\alpha) = b \cos(\alpha) + c\)

Custom MATLAB scripts were developed to perform nonlinear curve fitting, compute residuals, and evaluate goodness of fit using the coefficient of determination (R²).

Key Results

Lambert’s Cosine Law: Strong agreement with experimental data, achieving R² = 0.927, confirming angular dependence of irradiance.
Inverse-Square Law: Qualitative agreement observed, though deviations from the ideal (1/r^2) trend occurred due to ambient light interference, alignment sensitivity, and the non-point nature of the light source.

Technical Contributions

Designed and implemented an Arduino LDR sensing circuit
Developed MATLAB models for curve fitting and validation
Performed experimental uncertainty analysis and diagnostics
Integrated hardware sensing with numerical modeling workflows

Conclusion

The experiment successfully validated Lambert’s cosine law with high accuracy and demonstrated qualitative inverse-square behavior under real-world constraints. This project highlights practical challenges in experimental physics while reinforcing core radiative principles through hands-on instrumentation and data-driven analysis.

Documentation