Chromatography would show that a sample of orange juice contains (at least) two yellow dyes.
Chromatography is a process that separates a sample substance by passing it in a solution through a medium where the components that make up said solution separate by moving at different rates. There are three main types of chromatography: Gas Chromatography (GC), High Performance Liquid Chromatography (HPLC) and Thin-Layer Chromatography (TLC).
To separate the dyes in orange juice, TLC would most likely be used. A diagram is shown below. Basically, the orange juice would be placed at the pencil line (origin line) and the solvent (most likely water, called the mobile phase) would move by capillary action up the stationary phase (the chromatography plate) and the orange juice would separate into dyes based upon the particular dyes attraction to either the stationary or mobile phase.
So, if one of the dyes was more attracted to the mobile phase, it would move further and faster up the plate, whereas the other dye which is more attracted to the stationary phase would move slower and less distance than the other dye. This is also because the two dyes in question have different chemical structures, which alters the adsorption and desorption rates.