I'm trying to measure the $K_c$ of the equilibrium reaction
$$\ce{2 NO2 (g) <=> N2O4 (g)}$$
in different temperatures. How would I do this do this in a normal school laboratory? I was thinking of shining (laser) light through a test tube that contained $\ce{NO2 (g)}$ and looking at the intensity of light emitted. $\ce{NO2 (g)}$ is dark-reddish brown and $\ce{N2O4 (g)}$ is colorless. That means that the more to the right the equation is, the more light will be emitted.
However, I don't think this would give me accurate values for $K_c$. Are there any other methods that I could use to do this which preferably don't require advanced equipment (which I don't have)?