1. d is the distance between 2 slits, L is the distance between the slit and the viewing screen, P2 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 (P2) = 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 = P2 / 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 = 1010 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
