Light wave particle duality I have studied about the dual nature of light and all the experiments that proved light was a wave and sometimes a particle, and I am comfortable with the concept that it can be both. However, I have a few questions I am confused about.
1) If I have two different colours of light, I know that they are waves with different frequencies if I look at their wave nature, but what causes colour difference according to particle nature? Is it number of photons or energy that the photon contains?
2) according to wave nature, energy is proportional to amplitude of a wave. Does it mean a red beam of light can have more energy than another one if I increase its amplitude? And how do I increase its amplitude? (By shining more light?)
3) what exactly does amplitude and frequency correspond to in particle nature and wave nature and how do I physically see it (color, brightness, etc)
If some one could explain using analogies, that would be great.
 A: (1) it's the energy in the sense that the photon oscillates at a certain frequency.
(2) i'm not sure you can physically explain a light wave. More light is just more photons, more energy is photons with higher frequencies.
(3) when it comes to the particle nature of light the photon has a frequency. It frequently oscillates through positive and negative amplitudes as it travels along. As for the wave nature of light I'm not sure.
The color you see depends on the frequency of the photons. Our eyes have evolved to interpret these different frequency photons as different colors. Brightness depends on the number of photons.
A: In optics, you rather speak of intensity of light which is the energy per time and per surface. The brighter the light the more intensity it has. The energy transported by a light beam per minute is proportional to the squared amplitude of a wave or the number of photons times their energy.
$E\propto |E_0|^2$ for waves and
$E=n \cdot E_{photon}=n \cdot h \cdot f$ (h is the Planck constant)
To increase the intensity of a light beam, you can either increase the number of photons emitted per second or you can increase the frequency of light. In both cases it will increase the amplitude of the electromagnetic wave.
To make confusion perfect, sometimes the energy of single photon does matter and only increasing their number wouldn't help (photons don't "arrive" at exactly the same time so if a certain threshold energy is needed for a specific process, you can't just add up their energies). A classic example is the photoelectric effect which got Albert Einstein his Nobel Prize
