A sodium-vapour lamp illuminates, with monochromatic yellow light, two narrow slits that are 1.00 mm apart. if the viewing screen is 1.00m from the slits and the distance from the central bright line to the next bright line is 0.589 mm, what is the wavelength of the light?
To find the wavelength of the light, we can use the equation derived from the double-slit interference pattern:
λ = (d * x) / L
Where:
λ is the wavelength of the light
d is the distance between the two slits
x is the distance from the central bright line to the next bright line
L is the distance from the slits to the viewing screen
Given values:
d = 1.00 mm = 0.001 m
x = 0.589 mm = 0.000589 m
L = 1.00 m
Substituting these values into the equation:
λ = (0.001 m * 0.000589 m) / 1.00 m
λ = 0.000000589 m
Therefore, the wavelength of the light emitted by the sodium-vapour lamp is approximately 0.000000589 meters or 589 nm (nanometers).