Lambert’s cosine law example

Lambert’s cosine law, also known simply as the cosine law of illumination, describes how the intensity of light illuminating a surface changes based on the angle of incidence. Specifically, the law states that the intensity of light on a surface is directly proportional to the cosine of the angle θ between the direction of the incident light and the normal (perpendicular) to the surface.

Lambert’s cosine law example

Lambert’s Cosine Law: �=�0×cos⁡(�)I=I0​×cos(θ) Where:

• $I$ = Intensity of light on the surface.
• �0I0​ = Intensity of light when �=0∘θ=0∘ (i.e., when the light is perpendicular to the surface).
• $\theta$ = Angle between the direction of the incident light and the normal to the surface.

Example: Imagine a flashlight shining directly downwards onto a table. The light beam is perpendicular to the table’s surface, so �=0∘θ=0∘. In this case, the light’s intensity on the table, $I$, would be the maximum possible, �0I0​.

Now, if you start tilting the flashlight so that it’s no longer pointing straight down, but instead at some angle, the area it illuminates becomes larger and the light becomes dimmer. This is because the light is now spread over a larger area. The decrease in intensity can be predicted by the cosine of the angle at which the flashlight is tilted relative to the table’s surface.

For instance, if you tilt the flashlight to an angle of �=60∘θ=60∘ relative to the table’s normal, the intensity on the table would be: �=�0×cos⁡(60∘)I=I0​×cos(60∘) �=�0×0.5I=I0​×0.5 So, the intensity would be half of what it was when the flashlight was pointing directly downwards.

Applications in Everyday Life:

1. Photography: When setting up studio lights, understanding this law helps photographers to control the intensity of light on the subject by adjusting the angle of the lights.
2. Computer Graphics: In rendering realistic images, software often takes into account the angle at which light hits surfaces to determine the correct brightness and shading.
3. Solar Panels: The efficiency of solar panels is influenced by the angle of incidence of sunlight. Panels are often oriented to maximize the directness of sunlight, especially in tracking systems.

Conclusion: Lambert’s cosine law is a fundamental principle that explains the relationship between the angle of incident light and the illumination of a surface. Whether you’re a photographer looking to get the lighting just right or simply someone curious about why a flashlight’s beam spreads out when tilted, this law provides the answer.