All electrical laws
Lambert's cosine law
Also known as the Cosine law of illumination.
When light strikes a surface at an angle, the illuminance is reduced by the cosine of the angle between the ray and the normal to the surface.
E = (I / d²) × cos θ
- E
- illuminance on the tilted surface (lux)
- θ
- angle between the light ray and the surface normal
- I, d
- intensity (candela) and distance (metres) as before
In plain English: Tilted light smears over more area, so it's dimmer — the same reason winters are cold: the sun's rays arrive at a slant. At the point directly below a streetlight θ = 0 and you get full brightness; down the road it falls off fast.
Where you'll meet it: Streetlight spacing design, combining with the inverse square law for the standard 'illumination at a point away from the lamp post' problem (E = I·cos³θ/h² form).
Calculators that use this law
Components this law governs
Solar Cell / PhotovoltaicOutput follows the cosine of the angle between the sun and the panel normal, which is why tilt and orientation matter as much as area.Solar Panel / ModuleOutput follows cos θ between the sun and the panel normal — the physics behind tilt angle, seasonal output and why trackers pay for themselves.LED Bulb / Tube / PanelA panel light's output at an angle follows cos θ, which is why beam angle decides whether lumens land where you need them.HID Lamp (Sodium / Metal Halide / Mercury)Away from directly beneath the pole the light arrives at an angle, so illuminance falls as cos³θ — which is what sets pole spacing.