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As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.01 mm apart and position your screen 3.09 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 639 nm . How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe

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Answer:

[tex]0.00195\ \text{m}[/tex]

[tex]0.00293\ \text{m}[/tex]

Explanation:

m = Order = 1

D = Distance between screen and slit = 3.09 m

d = Slit distance = 1.01 mm

[tex]\lambda[/tex] = Wavelength = 639 nm

Distance from the first bright fringe from the central bright fringe is given by

[tex]y=\dfrac{m\lambda D}{d}\\\Rightarrow y=\dfrac{1\times 639\times 10^{-9}\times 3.09}{1.01\times 10^{-3}}\\\Rightarrow y=0.00195\ \text{m}[/tex]

Distance from the first bright fringe from the central bright fringe is [tex]0.00195\ \text{m}[/tex]

Distance from the second dark fringe from the central bright fringe is given by

[tex]y=(m+\dfrac{1}{2})\dfrac{\lambda D}{d}\\\Rightarrow y=(1+\dfrac{1}{2})\dfrac{639\times 10^{-9}\times 3.09}{1.01\times 10^{-3}}\\\Rightarrow y=0.00293\ \text{m}[/tex]

Distance from the second dark fringe from the central bright fringe is [tex]0.00293\ \text{m}[/tex].

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