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A double-slit experiment is set up using red light (λ = 706 nm). A first order bright fringe is seen at a given location on a screen. What wavelength of visible light (between 380 nm and 750 nm) would produce a dark fringe at the identical location on the screen? λ =

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Answer:

λ = 470.66 nm

Explanation:

for bright fringe[tex]y_m = \frac{m\lambda D}{d}[/tex]

D= distance between slit and screen

d= distance between the slits

for first order bright fringe m = 1,

        [tex] y_1 = \frac{1\lambda D}{d}[/tex]

         [tex]y_1 = {706*D}{d}[/tex]

for dark fringe,we have

[tex]y_m = {(m + 1/2)\lambda D}{d}[/tex]    

Now to get the dark fringes at the same location we should have;

(706)D/d = (m + 1/2)λD/d    

put m = 1

(1 + 1/2)λ = (706)

λ = 470.66 nm

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