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So I am wondering whether it would be possible to create an optical system that does and consists of the following: Use a Fresnel lens to concentrate direct sunlight to a point focus. I assume that the light will start diverging after the focus point where the incident rays converged to. If that is the case I can I simply collimate the diverging concentrated rays like I would collimate diverging rays from a normal point source as described in 2. of https://www.newport.com/n/focusing-and-collimating.

The idea is to use a second Fresnel lens to collimate the rays forming a beam of "concentrated" light.

The question is whether this is possible and if it is, will the resultant beam be "concentrated" as well?

Many thanks.

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You can form a small image of the sun, and then collimate the light from that image, but the image will not be infinitely small. Perhaps the simplest way to understand why this is so is to realize the sun has an angular extent in the sky. Using the common language, the sun is an "extended source". When you form an image of that extended source with a lens, the image will always have some finite extent. If you look at the Newport page you cited, Application 4 (Figure 6) is exactly what you would be doing with a lens. The diameter of the sun would be $2*y_1$, and the diameter of the image of the sun would be $2*y_2$. The picture is misleading because it is not to scale (obviously), but the relationships still apply in any imaging situation.

You can collimate the light from the image of the sun - but because the image that you made has a finite extent, the collimated beam formed will have some angular spread - it will not be "perfectly" collimated. This is intended to be shown by Application 2 (Figure 6) in the Newport article you cite, but this drawing is actually drawn by someone who did not understand the ray paths. The blue ray from the top of the object $y_1$ will actually head down, not up. However, they are are correct that the divergence angle $\theta_2 = y_1 * f$. It should be noted that this is the half-divergence angle, the full angular divergence is twice as much. It is common to confuse the two.

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No, you cannot

If by "point" you mean "a projected image of the Sun that is infinitely small", created by using an optic system that is not infinitely small, and not infinitely close to the target image, then the answer is an outright: no, that cannot be done.

There are several reasons for this.

1. Every valid optic system must be reversible

If you could create an infinitely small point of light from the rays of the sun, then you would have been able to create an image of the sun from an infinitely small point of light. But an infinitely small point of light has no discernible features. You cannot create a specific image from a non-specific light source.

A consequence of that optic systems by necessity must be reversible is Conservation of Étendue.

2. Thermodynamics prevents it

Incoming light that is at least partially absorbed by a target will give energy to that target. An infinitely small target would by that heat up to an infinite amount of degrees. Since the Sun is colder than infinity degrees, this would mean an energy transfer from a colder system to a hotter. This cannot happen.

3. Every optic system no better than a pinhole camera

The most perfect lens is an infinitely small pinhole. No optic system can ever deliver a more focused image than that. The pinhole cannot deliver an infinitely small image, unless the light source is infinitely small or the pinhole is infinitely close (distance = 0) to the target surface.

Every mirrored and/or refractive surface will result in an image that is "fuzzier" than a pinhole lens, and this rule includes Frenzel lenses. An image that is less focused than a perfectly focused image cannot be smaller than the perfectly focused image. An infinitely small point image of light source must by necessity be smaller than the perfectly focused image of its light source, as when created by a pinhole. This therefore is a contradiction, and thus not possible.

Source

xkcd what-if 145: Fire From Moonlight

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See application #2, you can collimate light from a "point" source. It is just the opposite of focusing collimated light.

https://www.newport.com/n/focusing-and-collimating

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