In general, a higher number of photons does indicate a brighter light. Photons are the individual particles or packets of energy that make up light. When more photons reach our eyes, we perceive the light as being brighter.
However, it's important to note that brightness is not solely determined by the number of photons. The energy or intensity of each individual photon also plays a role. For visible light, intensity is related to the amplitude or height of the light's electromagnetic wave. A larger amplitude corresponds to a higher intensity and a brighter light.
Regarding the comparison between violet and red light, violet light generally has a higher frequency and shorter wavelength than red light. This means that violet light carries more energy per photon than red light. Therefore, if we compare equal numbers of photons in violet and red light, the violet light will have a higher total energy and can appear brighter.
It is possible for different red lights to have different amplitudes. The amplitude of a wave corresponds to its maximum displacement from the equilibrium position. In the context of light, a higher amplitude means a greater maximum intensity or brightness. So, if two red lights have different amplitudes, the one with the higher amplitude would be perceived as brighter.
It's worth mentioning that the perception of brightness can be influenced by other factors as well, such as the sensitivity of our eyes to different wavelengths and the overall lighting conditions.