An Introduction to the Study of Light

The Wave Nature of Light
The wave properties of electromagnetic radiation are described by two interdependent variables: frequency and wavelength (and amplitude). The frequency and wavelength denote a particular color while the amplitude describes its intensity.

The Distinction Between Energy and Matter
Light (energy in the form of a wave function) and particles (matter) both behave in different fashions.
When a light wave passes from one medium into another, it undergoes the process of refraction and, consequently, changes the direction to which it is moving and continues to move in a straight line; whereas, when a particles passes from one medium into another, it does not change its path, but instead, begins to slow down and follows a curved path due to gravity (or any other strong gravitational force that is present).
When a light wave passes through a small hole it undergoes the process of diffraction; whereas, when a particle passes through a small hole it simply continues to move along its given path in a more or less straight line.
When a light wave passes through two small holes and strikes a screen it creates a multitude of vertical beams of light (dark lines are created when the waves are out of sync and the light lines are created when the waves are in sync. This process is called the process of interference); whereas when particles pass through adjacent openings, they continue in straight paths, some colliding with each other and moving at different angles.

Blackbody Radiation and the Quantization of Energy
When a solid object is heated it tends to emit visible light. Planck created the theory that an atom changes its energy state by emitting (or absorbing) one or more quanta (energy packets) and the energy of the emitted (or absorbed) radiation is equal to the difference in the atom's energy.
∆E(atom) = E(emitted or absorbed) = ∆nhv
h = Planck's constant.
v = is the wavelengths frequency.
n = quantum number of the element.
Since the change in its energy is only by integer multiples of hv, the smallest change occurs when an atom in a given energy state changes to an adjacent state, that is, when ∆n =1:
∆E = hv
h = Planck's constant.
v = frequency.
The later of the two formulas is the one to be used in this course.

The Photoelectric Effect and the Photon Theory of Light
Despite the fact that energy is quantized, many scientists kept to the energy traveling in the form of a wave model. The problem that arose is that the wave model of energy could not explain the photoelectric effect. The odd characteristics of the photoelectric effect are as follows:
1. Presence of a threshold frequency: Light shining on a metal must have a minimum frequency or else there will be no current flow.
2. Absence of a time lag: Current flows the moment light of this minimum frequency shines on the metal regardless of the light's intensity.
The main problem with the wave theory is that it focused on a minimum amplitude instead of frequency and upon the principle that the metal "stored" the energy and then once it reached its peak, current began to flow which is not held to be true.
A minimum frequency must be reached because, according to the photon theory (Einstein), a beam of light consists of an enormous number of photons. Light intensity (brightness) is directly related to the number of photons striking the surface per unit time but not their energy. Therefore a photon of a certain minimum energy must be absorbed for an electron to be freed.
The absence of a time lag can be explained as follows: An electron cannot "store" energy until it has enough to break free. An electron can only break free once it absorbs enough energy from one photon. Think of it this way, if electrons stored energy and broke free once they absorbed enough energy then every electron on this planet would break free just from the sun shining light upon the earth all day.