Question

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

Answer 1

`0.00195\ \text{m}`

`0.00293\ \text{m}`

Step-by-step explanation:

m = Order = 1

D = Distance between screen and slit = 3.09 m

d = Slit distance = 1.01 mm

`\lambda` = Wavelength = 639 nm

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

`y=(m\lambda D)/(d)\\\Rightarrow y=(1* 639* 10^(-9)* 3.09)/(1.01* 10^(-3))\\\Rightarrow y=0.00195\ \text{m}`

Distance from the first bright fringe from the central bright fringe is
`0.00195\ \text{m}`

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

`y=(m+(1)/(2))(\lambda D)/(d)\\\Rightarrow y=(1+(1)/(2))(639* 10^(-9)* 3.09)/(1.01* 10^(-3))\\\Rightarrow y=0.00293\ \text{m}`

Distance from the second dark fringe from the central bright fringe is
`0.00293\ \text{m}`.