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

Answer:

$0.00195\ \text{m}$

$0.00293\ \text{m}$

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

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

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

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

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