Rainbow, glory and orbiting scattering are usually described by the properties of the classical deflection function related to the real part of the quantum mechanical scattering phase shift or by the diffractive pattern of the quantum mechanical cross sections. Here we show that the case of orbiting scattering of massless spin 0, 1 and 2 particles from Schwarzschild black holes can be characterized by a sudden rise in $|{R}_{l}{|}^{2}$ at a critical angular momentum ${l}_{C}$, which we show corresponds to the unstable circular orbits of these particles. For the cases $s=0$, 2, we attempt a new interpretation of the Regge-Wheeler potential by identifying the quantum mechanical corrections to the effective potential of massless particles. We probe into the black hole scattering by using numerical and semi-analytical methods which give very good agreements with the exact numerical results. The limitations of previously used approximations as compared to the exact and semi-analytical results are discussed.