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# Optics Calculators

## Light

Light has properties and characteristics of both a particle and a wave. They have energy and momentum like a particle, and wavelength and frequency like a wave. In actuality other particles, such as electrons, can also behave as waves , but light is unique in that it is a particle (photon) with zero mass.

On a quantum level, photons are the mediators of the electromagnetic force. That is, they are exchanged by interacting charged particles and carry with them an electromagnetic field.

As waves, rays of light will be reflected, refracted, or diffracted when encountering an interface of two different materials.

### Frequency, Wavelength, Energy of light

Waves of light can be described in part by their energy, frequency and wavelength, which are all interrelated through fundamental constants:
$$f = c/\lambda \;\; \text{or}\;\; f = E/h \; \; \text{or}\;\; E = hc/\lambda$$

$$c$$ = 3x108m/s, is the speed of light
$$h$$ = 6.63x1034J s = 4.13566733×10−15 eV s, is Planck's constant

 $$f$$ ? Frequency is how often an event occurs per unit time. For light, it describes oscillation rate of the electromagnetic field. SI units: 1 Hertz = 1 Hz = 1/second. $$\lambda$$ ? Wavelength is the distance at which the wave repeats, e.g. the distance between two adjacent peaks or two adjacent troughs. SI units: meters $$E$$ ? Energy, or radiant energy, is a basic property of a particle or wave, and is always conserved in a closed system. SI units: joules (J), although small particles and light are often given in electron volts (eV). THz GHz MHz kHz Hz cHz mHz μHz nHz pHz km m cm mm μm nm eV keV MeV GeV J

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λ = 380 700 nm

For visible light, the frequency determines its color. The wavelengths of visible light span ~400 nm to 700 nm, corresponding to frequencies 7.4948x108 MHz to 4.2827x108 MHz and the rainbow of colors from violet to red.

The calculator above is for light in a vacuum. Light travelling through a medium will typically slow down (substitute $$v$$ for $$c$$ where $$v \lt c$$), and because energy is conserved, the wavelength will also change slightly. This is how refraction works, and why rainbows are made.

Visible spectrum, linear in wavelength (nm)

Visible spectrum, linear in frequency (THz)

### Interference / Diffraction

Interference occurs when two waves superimpose, such that their waves are added to form a combined wave. Depending on the relative amplitude, wavelength, and phase, the resulting wave can be larger, smaller, or some combination. Interference is usually most interesting when considering waves of very similar wavelength, often those originating from the same source and correlated. Interference can occur with any type of wave not just light.

When two waves with the same wavelength combine, the amplitude of combined wave is the sum of the two waves. If they happen to be in phase, the amplitude doubles. This is called constructive interference. If they are 180° (= π/2 radians) out of phase, the amplitude is zero. This is called destructive interference.

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