In general, the luminous intensity of a point on a surface varies by direction; for a Lambertian surface, that distribution is defined by the cosine law, with peak luminous intensity in the normal direction. Thus when the Lambertian assumption holds, we can calculate the total luminous flux, F tot , from the peak luminous intensity, I max , by integrating the cosine law: F tot = ∫ ∫ 0 2 π π ∫ ∫ 0 π π / 2 cos ⁡ ⁡ ( θ θ ) I max sin ⁡ ⁡ ( θ θ ) d θ θ d ϕ ϕ = 2 π π ⋅ ⋅ I max ∫ ∫ 0 π π / 2 cos ⁡ ⁡ ( θ θ ) sin ⁡ ⁡ ( θ θ ) d θ θ = 2 π π ⋅ ⋅ I max ∫ ∫ 0 π π / 2 sin ⁡ ⁡ ( 2 θ θ ) 2 d θ θ and so