Particles smaller than the wavelength of light

[Repetit]

Why exactly is it that ordinary light cannot be used to detect particles which are smaller than the wavelength of light? It seems logical somehow, that you cannot use a large "tool" to detect small particles, but what is the physical explanation to this??

Thanks in advance!

 

[vanesch]

Why exactly is it that ordinary light cannot be used to detect particles which are smaller than the wavelength of light? It seems logical somehow, that you cannot use a large "tool" to detect small particles, but what is the physical explanation to this??

First of all, you CAN detect small particles using big wavelength. Only, you will not learn anything about their small-ness and their structure, or their precise position. The essential explanation for it is the scattering of a plane wave by a potential well. It turns out that, if the size of the potential is much smaller than the wavelength of the incoming plane wave, that you get out essentially a spherical scattered wave, with not much structure to it (not much variation of intensity wrt spherical angle). So that's the same result as scattering from a Dirac pulse (= from a point). Also, because of the smoothness of the spherical outgoing wave, it will not differ much when you shift a bit the position of the scatter center. So you will not learn much about the exact position either.

 

[HallsofIvy]

Imagine trying to decide exactly what a small object is like, blindfolded, while wearing BOXING gloves. It would not be hard, even with the boxing gloves, to get an idea of the shape of a large object. But you couldn't even feel, say, an indentation smaller than your gloves.

Visible light will tell us about objects in units that are multiples of the wave length. For objects that are themselves smaller than that wavelength we just don't see anything but a blur.

Of course, if we extend from "visible light" to any electro-magnetic wave, we can get arbitrarily small wave lengths. Unfortunately, the energy in the wave increases in inverse proportion to the wavelength. If we use a wave with small enough wave length to get good information about the size and shape of a small object, we are giving it one heck of a kick!

 

[jtbell]

Consider an analogy with water waves. Suppose that you have waves traveling across the surface of a pool of water, with a wavelength of one foot (30 cm). Now suppose that these waves encounter a pencil with a diameter of about 0.5 cm, oriented vertically. How much does this single pencil affect the propagation of the waves?

 

[Claude Bile]

Why exactly is it that ordinary light cannot be used to detect particles which are smaller than the wavelength of light? It seems logical somehow, that you cannot use a large "tool" to detect small particles, but what is the physical explanation to this??

Thanks in advance!

You CAN use light to detect objects much smaller than its wavelength, with great detail too I might add. For example Ruiter et al, (Applied Physics Letters, 71, 28-30) detected a 1.5 nm long strand of DNA using optical wavelengths using a technique called Near-field Scanning Optical Microscopy (NSOM).

NSOM is a technique whereby the limits one normally encountered in the far-field (as mentioned below) are circumvented to a degree. In the near-field resolution is limited only by probe-sample separation and not wavelength as is the case in the far-field. The technique is not all that dissimilar to STM and other AFM imaging techniques.

Claude.

 

[uknova]

Could u not shoot waves with higher frequencies than visible light at it as a kind of radar (gamma rays?) to detect a shape in a bit more detail.

 

[HallsofIvy]

Yes, but as I said above, since the energy of an electromagnetic wave is inversely proportional to to its wavelength, You are hitting that small object with higher energy waves and so knocking it away- hence the Shroedinger uncertainty relation.

 

[ubavontuba]

Here's a related question:

What are the energy and wavelength limitations of light? If say you were to project the lowest energy light beam possible from a fixed location and then accelerate away from that location traveling along the beam, what would happen? Would the beam always be hypothetically detectable?

Is it possible for the energy level to drop so low that spin might be affected?

What are the upper limits? If you were to project the highest energy beam possible and then accelerate toward it, what would happen?