Direct Observation of Charge and Orbital Ordering in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>La</mml:mi></mml:mrow><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>1.5</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>MnO</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Charge ordering and orbital ordering in ${\mathrm{La}}_{0.5}{\mathrm{Sr}}_{1.5}{\mathrm{MnO}}_{4}$ have been investigated by using synchrotron x-ray diffraction. The alternating pattern of ${\mathrm{Mn}}^{3+}/{\mathrm{Mn}}^{4+}$ in real space is observed directly by making use of their anomalous dispersion. The first clear evidence of the orbital ordering of ${e}_{g}$ electrons on ${\mathrm{Mn}}^{3+}$ is also presented based on the measurements of ATS (anisotropy of the tensor of susceptibility) reflection near the Mn $K$-absorption edge. The present observations indicate that the charge ordering and orbital ordering occur simultaneously at a transition temperature higher than that of the spin ordering.