When comparing two light sources, for example, a light bulb at 20W and a light bulb at 100W, what is it about the incoming light that makes the latter look brighter than the former? Are there different reasons why different light sources looks different in brightness (High five for cramming three instances of "different" in the same sentence)? For example, in this thread, it is stated that the human eye is most sensitive around 555nm, something that I guess translates to meaning that given a light of the same intensity (whatever that means, hence my question), it is going to be perceived as most bright when hitting 555nm. Does this question have different answers depending on if you're seeing light as a particle vs a wave?
The 100 W light bulb dissipates more energy per second (1 watt = 1 joule per second) than the 20 W light bulb, and consequently the light emanating from the 100 W bulb carries more energy than the light emanating from the 20 W bulb.
In the picture of light as an electromagnetic wave, the energy carried by the light is proportional to the square of the wave's amplitude. The technical term for this energy is "Poynting flux". (In fact we usually take the time-average over one period of oscillation as the definition of the energy in the wave.) In this model, the photo-receptors in your eye are oscillators. What is oscillating? Electric charge. Charges are accelerated in response to the electric field of the light: the greater the electric field (or amplitude), the greater the amplitude of the oscillation, and the greater the electric currents in your eye (and the greater the brightness).
In the picture of light as a particle (a photon), each particle carries with it an amount of energy proportional to its frequency: $E=h\nu$, where $h$ is Planck's constant, and $\nu$ is the frequency of light. The energy flux is then the energy per photon multiplied by the flux of photons (# of photons per unit area per second). So the 100 W bulb emits more photons per second than the 20 W bulb. In this model, the photoreceptors in your eye undergo chemical reactions as a result of absorbing photons. The more photons absorbed per second, the brighter the light appears.
Brightness is just the number of photons per second hitting your eye - all the other properties of the light are the same.
edit: perceived brightness is the number of 'detected' photons hitting your eye per second!
Different wavelengths of light correspond to different colours. 555nm means light with a wavelength of 555 nano-meters (billions of a meter), this is roughly green light. So all this says is that you eye is most sensitive to green light and so a given number of green photons/second will appear brighter than the same number of red photons. You can see this with laser pointers, for the same power small pointers - green ones look much brighter than red.
I am nowhere near as expert as a professional, but I have a private passion for this field.
Dim and bright are perceptual terms. There are many dimensions. I will start with a simple idea and build out.
Consider that you are adapted to a monochromatic light of around 533 nanometer wavelength bathing the room such that the light from the brightest object generates approximately 1e7 photons per second on a foveal L cone of 1 micron face diameter. This is considered a well-lit but not stressful scene. The photoreceptor opsins bleach at a rate of approximately 5e3 opsins per second. The light feels neither dim nor bright because you are adapted.
If you increase the source photon rate by a factor of 10, that same photoreceptor is now bleaching at a rate of 5e4 opsins per second. This feels brighter. But over time, the photoreceptor undergoes phagocytosis, decreasing its length by 90% changing the opsin bleach rate back to 5e3 opsins per second, so you now experience this as neither dim nor bright.
If you decrease the wavelength to 430 nanometers, the bleach rate of the L cone decreases by 90% and one would think this would appear dim. However, the S cone bleach rate reaches its maximum and S cones have a stronger effect on perceived brightness than L cones, so without increasing the photon bleach rate, the light now appears to have gotten brighter.
This is the principal reason amber sunglasses make the world seem brighter and more colorful. By suppressing the short wavelength photons from reaching the eye, the adaptation of the L and M cone bias favors a greater linear range. This makes colors more discriminable and is another dimension of brightness.
I will leave these three dimensions for further discussion and, if requested, I will dive deeper yet into the wonderful world of retinal adaptation to various light regimes.