Question

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 =

Answer 1

λ = 470.66 nm

Step-by-step explanation:

for bright fringe
`y_m = (m\lambda D)/(d)`

D= distance between slit and screen

d= distance between the slits

for first order bright fringe m = 1,

`y_1 = (1\lambda D)/(d)`

`y_1 = {706*D}{d}`

for dark fringe,we have

`y_m = {(m + 1/2)\lambda D}{d}`

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