If light is at an angle the light is not as direct so we account for that scaling down the light. This is done by multiplying by the cosine of the normal of the surface to the angle of the light direction.

JiaweiChenKodomo

It is that only $\Phi cos(\theta)$ light flux reaches the surface that causes the reduction in irradiance.

andrewdotwang

To simple things up, we could think of cos(theta) * A as the difference between the the most right and left points on the surface.

If light is at an angle the light is not as direct so we account for that scaling down the light. This is done by multiplying by the cosine of the normal of the surface to the angle of the light direction.

It is that only $\Phi cos(\theta)$ light flux reaches the surface that causes the reduction in irradiance.

To simple things up, we could think of cos(theta) * A as the difference between the the most right and left points on the surface.