A beam of $\mathrm{\alpha }-$ particle is incident on a gold foil. Corresponding to the incident beams $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ , the emergent beams ${\mathrm{A}}^{\mathrm{\prime }},{\mathrm{B}}^{\mathrm{\prime }}$,and ${\mathrm{C}}^{\mathrm{\prime }}$ . The transmission and deflection of $\mathrm{\alpha }-$ particles through the foil take place such that