# 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.

(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.

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

• '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.'. If I change the frequency of light, won't I just be changing the colour? For example, yellow light may become blue but will remain just as bright as it was before. Nov 10, 2015 at 15:26
• Yes, for your eye it would just turn blue. The sensitivity of your eye depends on the frequency of the light. It is much most sensitive to green light. en.wikipedia.org/wiki/Spectral_sensitivity Nov 10, 2015 at 15:43
• Exactly. So if I've followed this discussion correctly, changing frequency of light DOES NOT affect brightness at all. Physically, it only changes the colour. From the quantum theory point of view, each photon now has a little more energy than before, number of photons remaining constant. But since the brightness is the same, the intensity was not affected. (Correct me if I went wrong anywhere.) Nov 10, 2015 at 15:49
• Intensity is the energy per unit time and surface. So a higher frequency results in more energy per time and surface, so the intensity is higher as well. What is brightness for you? If you take luminosity, this value is correct for the specific sensitivity of the human eye. Nov 10, 2015 at 16:20
• The cones in our eyes have evolved to make greenlight more sensitive than red or blue but the brightness or intensity is determined by the number of protons. Nov 10, 2015 at 16:47