As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.15 mm apart and position your screen 3.93 m from the slits. Although Young had to struggle to achieve a monochromatic light beam of sufficient intensity, you simply turn on a laser with a wavelength of 647 nm . How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe

a) y = 2.21 10⁻³ m, b)  y = 5.528 10⁻³ m

Explanation:

In the double-slit experiment the interferences occur at the positions

         d sin θ = m λ                    constructive interference

         d sin θ = (m + ½) λ           destructive interference

let's use trigonometry for the angle

          tan θ = y / L

as in this experiment the angles are very small

          tan θ = sin θ/cos θ = sin θ

          sin θ = y / L

we substitute

         d y / L = m λ                   constructive interference

         d y / L = (m + ½) λ          destructive interference

Let's answer the questions

a) first line of constructive interference me = 1

          y = m  λ L / d

          y = 1 647 10⁻⁹ 3.93 /1.15 10⁻³

          y = 2.21 10⁻³ m

b) second dark band m = 2

            y = (m + ½) λ L / d

            y = (2 + ½)  647 10⁻⁹ 3.93 /1.15 10⁻³

            y = 5.528 10⁻³ m

pecialized keyboards

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”.

hope this !