How do scientists know that light has a dual wave-particle nature? In what ways does light behave as wave and particle?

The double-slit experiment shows that it acts as both a wave and a particle. Look that up on google or something for more information.

http://en.wikipedia.org/wiki/Double-slit_experiment

Wave nature:

If we analyze a beam of light with a double slit or a diffraction grating, we get an interference pattern (colored light fringes) which is consistent with the wave nature of light. We can perform measurements on the interference pattern and calculate wavelengths. That is relatively easy.
Particle nature
1. Black body radiation:
The particle nature of light was originally used as a hypothesis to explain why a hot glowing object does not give off light of equal intensities at different wavelengths (colors). Classical physics predicted That the energies emitted by light produced by a hot object at different colors should be equal. However, when a hot object just starts glowing most light emitted is infrared and red. The intensities decrease at higher frequencies (green, blue, violet, ultraviolet, etc).
2. Photoelectric effect:
When light shines on a metallic surface, electrons are ejected. "Electric eye" devices are based on this effect. The number of electrons ejected depends more on the wavelength than the intensity of the light beam. Einstein showed mathematically how particles of light (photons) can explain this better than waves.

A couple of links for the particle nature of light that are relatively easy to follow:

(Broken Link Removed)

http://www.colorado.edu/physics/2000/quantumzone/photoelectric.html

The first link improved:

http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html

Scientists know that light has a dual wave-particle nature through a combination of experimental evidence and theoretical models.

One of the key experiments that supported the wave-particle duality of light was the double-slit experiment. In this experiment, a beam of light is shone at a barrier with two narrow slits. Behind the barrier, a screen is placed to detect the pattern of light passing through the slits. If light were only a particle, you would expect to see two distinct bands of light on the screen corresponding to the two slits. However, the experiment showed that light behaves as a wave, with an interference pattern of alternating bright and dark bands on the screen. This interference pattern is a characteristic of wave behavior.

Another experiment that demonstrated the particle nature of light is the photoelectric effect. This phenomenon occurs when light shines on a metal surface, causing the ejection of electrons. Albert Einstein explained this effect by proposing that light energy is quantized into discrete particles called photons. Each photon carries a specific amount of energy, and when it interacts with the metal surface, it can transfer its energy to an electron, causing it to be ejected. This observation of discrete packets of energy behaving as particles supports the particle nature of light.

In summary, light exhibits wave-like behavior in phenomena such as interference patterns, while also displaying particle-like behavior in the photoelectric effect. The wave-particle duality of light is a fundamental principle of quantum mechanics and is supported by a range of experimental and theoretical evidence.