The simplest example illustrating the use of the impact parameter is in the case of scattering from a sphere. Here, the object that the projectile is approaching is a hard sphere with radius R . In the case of a hard sphere, U ( r ) = 0 when r > R , and U ( r ) = ∞ ∞ for r ≤ ≤ R . When b > R , the projectile misses the hard sphere. We immediately see that θ θ = 0 . When b ≤ ≤ R , we find that b = R cos ⁡ ⁡ θ θ 2 .