Light with a wavelength (a) At what distance from the center of the screen will the second dark fringe appear?

Question

Light with a wavelength of 673 nm (6.73 x 10-7 m) is incident upon a double slit with a separation of 0.5 mm (5 x 10-4 m). A screen is located 7.3 m from the double slit.
(a) At what distance from the center of the screen will the second dark fringe appear?

Answer 1

λ = 6.73 x 10^-7 m

d = 5 x 10^-4 m

L = 7.3 m

 

For a dark fringe, the distance from the centerline is 

 

y = (λL/d)(m + 1/2),

 

m = 0, ±1, ±2, ±3, ...

 

The 2nd dark fringe corresponds to m = 1 ⇒ 

 

y₂ = (3/2)λL/d = 1.5(6.73 x 10^-7 m)(7.3 m) / (5 x 10^-4 m) ≅ 14.74 mm