Irina finds an unlabeled box of fine needles, and wants to determine how thick they are. A standard ruler will not do the job, as each needle is less than a millimeter thick. So, to find the thickness, she uses a needle to poke a hole in a piece of brown construction paper. Then, she positions a 657 nm laser pointer to shine through the hole and project a circular diffraction pattern on a wall 22.2 m away. She then uses her ruler to measure that the central bright circle is 12.2 cm in diameter. What diameter does Irina calculate for the needle?

To solve this problem we will first determine the position of the first minimum and then use the Rayleigh for resolution criterion. The criterion basically says that the diameter is equivalent to 1.22 the product of the wavelength by the circular diffraction pattern at the rate of the first minimum. The first minimum for its part is the middle of the central bright circle. So, position of first minima,

Diameter of needle (formula from Rayleigh's criteria for resolution),

Therefore the diameter that Irina calculate for the needle is

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

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