Why is the photosynthetic pigment extract green under light transmission and dark red under light reflection?

When observing the chlorophyll extract in the light source, what you see is the absorption spectrum of chlorophyll. Because chlorophyll extract absorbs the least green light, what is observed by naked eyes is green transmitted light.

When the chlorophyll extract is observed by backlight, it will see the emission spectrum produced by excited chlorophyll molecules. After absorbing photons, chlorophyll molecules rise from the most stable ground state with the lowest energy to the unstable excited state with higher energy. Because the excited state is unstable, it emits light waves (this light wave is fluorescence), and the energy disappears, and soon it returns from the excited state to the ground state. Some of the light energy absorbed by chlorophyll molecules is used for internal vibration of molecules, so the radiation energy is very small. Light propagates discontinuously in the form of photons, e = HV = HC/λ, that is, the wavelength is inversely proportional to the photon energy. Therefore, the wavelength of the reflected light wave is longer than the wavelength of the incident light wave, and the chlorophyll extract is red under the reflected light.

The phenomenon that chlorophyll solution is green under transmitted light and red under reflected light is called fluorescence.