# Uncertainty principle in classical optics

1. Mar 5, 2012

### ShayanJ

As you know,a pure sine wave extends infinitely in both directions and a wave which is the composition of some different frequencies,has a limited extent.Does it mean that such a wave is a pulse moving in space or it has limited range?(I know its crazy to talk about the range of light,but I've heard such interpretation from a professor)
thanks

2. Mar 6, 2012

### pabloenigma

I dont know what you mean by limited range.But it does definitely mean that Light is emitted in form of discrete pulses,and thats the reason that purely monochromatic sources are an idealization.This finiteness of the pulses give rise to what is known as the spectral spread about the mean frequency or whatever.

For details,look up for information on temporal coherence.

3. Mar 6, 2012

### chrisbaird

If you mean by "limited range" that a light pulse completely disappears at some distance, then this is wrong. We pick up light from the most distant objects in the universe just fine without the light running out of gas before it reaches us. If you mean that the light gets weaker as it travels, this is true. As light spreads out in all directions, the total electromagnetic field energy must be conserved over an ever expanding spherical wave front, so it must diminish in strength as it does so. That is why distant stars are so faint.

4. Mar 10, 2012

### marcusl

What you are describing (a collection of waves of slightly differing frequencies) is usually called a "wave packet", and yes, it has an approximately finite extent. It's not crazy to talk about it's extent--they are talked about in one real application, which is radar. A radar pulse is finite in both time and frequency (to within the usual approximations) so the expanding wave packet indeed has a length that can sometimes matter in detecting a target.

5. Mar 10, 2012

### mdabdullah270

In the classical electromagnetic theory the wave-vector k = (2π/λ)σ underlies the Fourier space of propagating (or radiative) fields. The k-vector combines into a single entity the wavelength λ and the unit vector σ that signifies the beam's propagation direction. The Fourier transform relation between the three-dimensional space of everyday experience and the space of the wave-vectors (the so-called k-space) gives rise to relationships between the two domains analogous to Heisenberg's uncertainty relations.