In this research, the interaction potential between a neutral polarizable particle and a semi-infinite dielectric medium is evaluated. In quadratic stark formula. the classical electric field is replaced by electric field operator and then the expectation value is taken with respect to vacuum state. By relating the electric field correlation function to the vector potential Green function (via fluctuation dissipation theorem), the interaction potential is written in terms of the vector potential Green function. Finally by computing the vector potential Green function at the presence a semi-infinite dielectric wall, the interaction potential is evaluated in terms of the particle polarizability, particle distance (to the wall) and the dielectric function of the wall. As the distance increases, the potential decreases, so the graph tends to go down.