# Young’s double-slit experiment – problems and solutions

1. d is the distance between 2 slits, L is the distance between the slit and the viewing screen, P_{2} is the distance between the second-order fringe and the center of the screen. Determine the wavelength of light (1 Å = 10^{-10} m).

__Known :__

Distance between two slits (d) = 1 mm = 1 x 10^{-3} m

Distance between slit and the viewing screen (L) = 1 m

Distance between the second-order fringe and the central fringe (P_{2}) = 1 mm = 1 x 10^{-3} m

Order (n) = 2

__Wanted :__ the wavelength of light (λ)

__Solution :__

__The equation of double-slit interference ____(____constructive interference____) __:

d sin θ = n λ

sin θ ≈ tan θ = P_{2} / L = (1 x 10^{-3}) / 1 = 1 x 10^{-3} m

__The wavelength of light :__

λ = d sin θ / n

λ = (1 x 10^{-3})(1 x 10^{-3}) / 2 = (1 x 10^{-6}) / 2

λ = 0.5 x 10^{-6} m = 5 x 10^{-7 }m

λ = 5000 x 10^{-10} m

λ = 5000 Å

2. Figure below shown result of a double-slit interference. Determine the wavelength of light (1 m = 10^{10} Å)

__Known :__

Distance between two slits (d) = 0.8 mm = 8 x 10^{-4} m

Distance between slit and the viewing screen (L) = 1 m

Distance between the fourth-order fringe and the central fringe (P) = 3 mm = 3 x 10^{-3} m

Order (n) = 4

__Wanted :__ The wavelength of light (λ)

__Solution :__

__The equation of double-slit interference ____(____constructive interference____) __:

d sin θ = n λ

sin θ ≈ tan θ = P / L = (3 x 10^{-3}) / 1 = 3 x 10^{-3} me

__The wavelength of light :__

λ = d sin θ / n

λ = (8 x 10^{-4})(3 x 10^{-3}) / 4 = (24 x 10^{-7}) / 4

λ = 6 x 10^{-7} m = 6000 x 10^{-10} m

λ = 6000 Å

3. Based on figure below, point A and B is the first two bright interference fringes and the wavelength of light is 6000 Å (1 Å = 10^{-10} m). Determine distance between two slits.

__Known :__

Distance between slit and the viewing screen (L) = 1 m

The wavelength of light (λ) = 6000 Å = 6000 x 10^{-10} m = 6 x 10^{-7} m

Distance between the first-order fringe and the central fringe (P) = 0.2 mm = 0.2 x 10^{-3} m = 2 x 10^{-4} m

Order (n) = 1

__Wanted :__ Distance between two slits (d)

__Solution :__

__The equation of constructive interference :__

d = n λ / sin θ

sin θ ≈ tan θ = P / L = (2 x 10^{-4}) / 1 = 2 x 10^{-4} m

__Distance between two slits :__

d = n λ / sin θ = (1)(6 x 10^{-7}) / (2 x 10^{-4})

d = (6 x 10^{-7}) / (2 x 10^{-4}) = (3 x 10^{-3})

d = 0.003 m

d = 3 mm