In the above picture of the microscope experiment, I am considering that the observer is situated at the eyepiece. The observer is a rectangular 2D grid of square-shaped detectors, each detector with a side length of $s$. The experiment is done with a single photon. If a photon encounters one of these square-shaped detectors, we get a reading of the coordinates of the location of that detector.
Now, if we increase the distance $a$ as shown in the figure, we can locate the position of the photon with less uncertainty as we are restricting the angular spread of the photon. As we increase the distance more and more, the uncertainity in position of detection of photon decreases less and less. Momentum of photon is fixed as we have monochromatic light of a definite wavelength, say the photon emitted from a specific atomic transistion. Since the collision is elastic, the wavelength of photon will remain the same. (Is this true?) Then, the uncertainity in the measurement of photon $\Delta p$ would be zero. So, the uncertainity in position must be infinite. But if we are at liberty to make $a$ as big as possible, there does not seem to a lower limit to $\Delta x$.
What is wrong with this argument?
