Place the object very far away from the lens, so that the object distance is as great as possible. The larger the object distance, the more insignificant is the difference between focal length and image distance.

in the image illustrated above, we obtain focused image at the (position of image, inverted yellow arrow) not at the focal point.

As others pointed out, the lensmaker's formula describes how the object $p$ and image $q$ distance are related to this property of the lens. So you just measure $p$ and $q$, and find $f$ from

Athermaltransformation

(I took the liberty of rearranging the usual formulation $\frac{1}{f}=\frac{1}{p}+\frac{1}{q}$ so you obtain $f$ directly from your measured values).

so my question is how this method is true since the image will not be formed at the focal point, instead it will be beyond the focal point,therefore the result of focal length obtained will be false, can anyone help me please?

to determine the focal length of the lens practically, we change the position of the image until we obtain a clear image which will be at the yellow arrow (not at focal point).

For dark matter direct detection searches, the resolution of the detector is not as important as its mass. The more atoms available to interact with dark matter, the better. But the larger the mass, the larger the heat capacity, and a larger heat capacity degrades energy resolution. You can operate the detector at a lower temperature to lower the heat capacity down, and that is the strategy employed by the CUORE and EURECA collaborations (we also the same strategy for our CUPID and Ricochet neutrino detectors). The CDMS collaboration developed the Quasiparticle-assisted Electrothermal-feedback Transition-Edge Sensor, or QET, in order to perform an athermal measurement of the recoil energy deposited in an event. An athermal measurement effectively decouples the heat capacity of the absorber (also called the "target") from the detector heat capacity, and also has faster time constants since you measure the energy of the ballistic phonons before they thermalize in the target crystal. An added benefit is that athermal phonons give you position information on the event, which allows you to fiducialize the volume and reject events near the surfaces of your detector. Both techniques have been shown to work, and although they have different optimizations, both thermal and athermal designs have been sucessfully deployed in dark matter searches.

Athermallens

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The lensmaker's equation, $\frac {1}{p} + \frac {1}{q} = \frac {1}{f}$ is all you need if you have p and q. Just solve it for $f$, which is the focal length (the distance from the lens to the focal point).

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In addition to the QETs, our dark matter detectors are connected to charge sensors to read out electron-hole pairs that are released during the recoil. The ratio of charge to phonon signals is different for nuclear recoils and electron recoils, and forms the main discriminator of bulk gamma events in our detectors.

The illustration above shows the main elements of the QET design. A crystal germanium or silicon absorber is held at low temperature (around 50 mK). On its surface are the QETs, which are composed of aluminum collection fins (shown in grey) connected to a TES (shown in light blue). The aluminum collection fin is superconducting at these temperatures, while the TES is biased and is thus in its transition. When a recoil event happens (labeled interaction site) phonons with a spectrum way out of equilibrium with the 50 mK crystal temperature propagate from the interaction site across the crystal. These athermal phonons anharmonically decay until they become ballistic, meaning that their mean free path is longer than the dimensions of the crystal. At that point, the phonons are still athermal, but rattle around the crystal as particles in a box. Phonons hitting aluminum collection fins are absorbed into them and break cooper pairs inside the superconductor, producing quasiparticles. These quasiparticles diffuse through the aluminum and make their way to the TES, where they release their energy and heat the TES up, producing a detectable signal. The reason for this complicated path is that the aluminum acts like a catcher's mitt to collect phonons, so that we can keep the heat capacity of the TES small (and thus retain good energy resolution) and at the same time have a significant fraction of the surface area of the crystal covered by phonon-collecting material.

One can also use Bessel's method, moving the lens between the two positions where there is a focused image (enlarged or smaller): $$f = \frac{D^2 -d^2}{4D},$$ where $D$ is the distance between object and image and $d$ the distance between the two ens positions.

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Better is to use a source of light that resembles a point source, such as the tip of an optical fiber, and place this at the focal length of a second lens so that a collimated beam is produced. Use the lens you are testing to focus the collimated beam to a point. The distance from the lens to the focus is the focal distance.

We call it the focal point - but most of the time it's not where the image is located. Once you understand you are dealing with a property of the lens, not of the imaging scenario, I think this will be clear.

The focal point is a property of the lens. It is where parallel light would converge (in practice, that is light that "appears to come from infinitely far away").