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We define a new thermospheric concept, the reference heights of O/N₂, referring to a series of thermospheric heights corresponding to the fixed ratios of O to N₂ number density. Here, based on Global Ultraviolet Imager (GUVI) limb measurement, we compare O/N₂ column density ratio (∑O/N₂) and the reference heights of O/N₂. We choose the transition height of O and N₂ (transition height hereafter), a special reference height at which O number density is equal to N₂ number density, to verify the connection with ∑O/N₂ during geomagnetically quiet periods. It is found that transition height and ∑O/N₂ have noticeable negative correlation with correlation coefficient of -0.887. An empirical model of transition height (O/N₂ model hereafter) is established based on nonlinear least-squares-fitting method. The considerable correlation (greater than 0.96), insignificant errors (less than 4\%) and the great influencing weight of ∑O/N₂ to reference heights indicate the validity of O/N₂ model and the existence of quantitative relation between ∑O/N₂ and transition height. Besides, it is verified that the similar quantitative relation also exists between ∑O/N₂ and reference heights of other O/N₂ values. Namely, using the O/N₂ model coefficients, we can roughly get the whole altitude profiles of O/N₂ within 6\% precision for any given ∑O/N₂.