The linear and third-order nonlinear optical absorption coefficients (ACs) and the refractive index change (RIC) for a spherical quantum dot, having a hydrogenic impurity under an applied magnetic field have been theoretically studied. In numerical calculations, a variational scheme is adopted within effective mass approximation to determine the energy eigenvalues for the impurtiy. The variations of impurity binding energy with the dot radius, the linear and nonlinear ACs and RIC with the photon energy are investigated and effect of homogeneous magnetic field strength is discussed on these optical properties. It has been found that the binding energy, ACs and RIC are sensitively dependent on the magnetic field strength. Moreover, the calculated results also indicate that the absorption peak energies move to higher energies with increasing magnetic field.