# What is a focal diameter

## Forum: HF, radio and fields Real focus size

Hello, It's about the following: Theoretically, the focal point of a converging lens should be infinitely small. Is that right so far? But how does it look in reality? If the focal point were really infinitely small, air could be ionized with any focused light source. You could then bring a certain power to an infinitely small point, which would then be enough to generate a plasma in the air. It is well known that this does not actually work. However, on various websites you can read that air can be ionized with appropriately strong and focused laser light, whereby the wavelength is not important. Nobbi

Alex W. wrote:> The focal point diameter is larger than the wavelength, thank you, I already suspected that. I still have one question: How big is the ionization energy of air, or how can I calculate it. Do I just have to calculate the various ionization energies of the "large" elements as a percentage?

Nobbi wrote:> Alex W. wrote: >> The focal point diameter is larger than the wavelength >> Thanks, I already suspected that. >> I still have one question: How big is the ionization energy of> air, or how can I use it to calculate. Do I just have to calculate the> different ionization energies of the "large" elements as a percentage? If you mean the air breakdown, e.g. to ignite a plasma with a laser, the energy is about 2GW / cm ^ 2! But since the laser is focused, the energy density increases. An energy of 14.534eV is needed for a piece of material molecule (75% of which are in the air). Assuming 600nm the laser has: E = h * v = 1eV = 1 602 * 10 ^ -19J h = 6.6262 * 10 ^ -34Js the energy density is decisive and not the wavelength. Here is a paper for the calculation: http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA133211

Nobbi wrote:> In theory, the focal point of a> converging lens should be infinitely small. Is that right so far? No. In theory, too, the spot is not infinitely small [*]. The size of the focal spot is limited by the size of the lens, even if the lens is perfectly ground. What the lens does is a 2D Fourier transform. A component of the wave spectrum, namely a direction, is mapped onto a point on the focal plane. The same uncertainty applies as with the 1D Fourier transform. Due to the finite expansion of the window (here the lens), the impulse (here the focal point) becomes wider. The larger the lens, the smaller the focal point. An infinitely small focal point (a point) would only produce an infinitely large lens. In optics this runs under the keyword "diffraction limitation". [*] Believe it or not, the theory can also deal with lenses of finite size.

The focal point is a scaled-down image of the light source. So if the light source has a finite size or the beam path was not exactly parallel before, the image is also finitely large. And vice versa, if the beam path is exactly parallel or the light source is point-shaped, Plasmon's statement regarding lens diameter applies ...

B e r n d W. wrote:> The focal point is a reduced image of the> light source. Now I have to get petty again, because here different things are mixed up, which in theory are neatly separated. The image of the source (or any object) is not "the focal point" but rather "the image of the source". What is called the focal point is really the image of a point (whether in the finite or in the infinite), so the point response of the imaging system "lens", so to speak. The image of the source is already composed of an infinite number of such pixels. The image sharpness depends on the extent of the image of a point (the point response). That is something different from the image expansion due to the expansion of the original image. In the case of a finitely large lens, the image has a finite extent, even if the original image is a point. This expansion naturally becomes even greater if the archetype also has an expansion. But I wouldn't use that to characterize a lens, because what one observes in an extended archetype is no longer the point response of the lens, but the imaging result of a real object.

Nobbi wrote: >> However, on various websites you can read that air can be ionized with correspondingly> strong and focused laser light, whereby the> wavelength is not important. So the wavelength already has an influence and you have to be able to focus your laser beam at some point and if you then absorb some dear molecules in the air on the way it will be difficult. However, you can also use these transitions in a targeted manner. It just depends on how the plasma wants to be generated (nonresonant / resonant breakdown). So thumb times pi are under normal conditions in the air like already said ~ 10 ^ 9 W / cm ^ 2. This can be achieved with a focused laser pulse of ~ 10ns and ~ 100uJ.

There are limits to a lens. Because with increasing curvature the reflection increases, ie towards the edge more and more reflection losses come into play. Therefore one should work with a small numerical aperture, a small angle. At most, a spherical mirror is better.

Nobbi wrote:> It is about the following: In theory, the focal point of a> converging lens should be infinitely small. This only applies to the simplified representation with ray optics. The actual phenomena are better described by wave optics and there is the effect of diffraction which makes the focal point the Fourier transform of your lens.

Plasmon wrote:> Nobbi wrote: >> In theory, the focal point of a >> converging lens should be infinitely small. Is that correct so far? >> No. In theory, too, the spot is not infinitely small [*]. The> size of the focal spot is limited by the size of the lens, even if> the lens is perfectly ground. Whereby "ideal" is not spherical, see spherical aberration.

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