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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 3.53 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

Respuesta :

Answer:[tex]y_1=1.9\ mm[/tex]

Explanation:

Given

slit width [tex]d=1.15\ mm[/tex]

Distance of screen [tex]D=3.53\ m[/tex]

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

Position of any bright fringe is given by

[tex]y_n=\dfrac{n\lambda D}{d}[/tex]

[tex]y_1=\frac{1\times 639\times 10^{-9}\times 3.53}{1.15\times 10^{-3}}[/tex]

[tex]y_1=0.0019\ m[/tex]

[tex]y_1=1.9\ mm[/tex]

Position of dark fringe is given by

[tex]y_D=\dfrac{(2n+1)\lambda D}{2d}[/tex]

for second dark fringe [tex]n=1[/tex]

[tex]y_D=\dfrac{1.5\times 639\times 10^{-9}\times 3.53}{1.15\times 10^{-3}}[/tex]

[tex]y_D=0.00294\ m\approx 2.94\ mm[/tex]

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