The structural colour of the neon tetra is distinguishable from those of, e.g., butterfly wings and bird feathers, because it can change in response to the light intensity of the surrounding environment. This fact clearly indicates the variability of the colour-producing microstructures. It has been known that an iridophore of the neon tetra contains a few stacks of periodically arranged light-reflecting platelets, which can cause multilayer optical interference phenomena. As a mechanism of the colour variability, the Venetian blind model has been proposed, in which the light-reflecting platelets are assumed to be tilted during colour change, resulting in a variation in the spacing between the platelets. In order to quantitatively evaluate the validity of this model, we have performed a detailed optical study of a single stack of platelets inside an iridophore. In particular, we have prepared a new optical system that can simultaneously measure both the spectrum and direction of the reflected light, which are expected to be closely related to each other in the Venetian blind model. The experimental results and detailed analysis are found to quantitatively verify the model.