n part A of the experiment a pair of slits are illuminated with a laser and an interference pattern is observed. The slit spacing is d = 0.0001 m and the pattern is projected on to the wall a distance L= 2.49 m from the slits. From one dark spot 8 further dark spots are counted and the distance is measured to be Z = 0.109 m.Calculate the wavelength λ of the laser.Express answer in nm (1x10-9m) to the nearest whole number.
Question
n part A of the experiment a pair of slits are illuminated with a laser and an interference pattern is observed. The slit spacing is d = 0.0001 m and the pattern is projected on to the wall a distance L= 2.49 m from the slits. From one dark spot 8 further dark spots are counted and the distance is measured to be Z = 0.109 m.Calculate the wavelength λ of the laser.Express answer in nm (1x10-9m) to the nearest whole number.
Solution
The formula for the interference pattern in a double-slit experiment is given by:
λ = (d * Z) / (m * L)
where:
- λ is the wavelength of the light,
- d is the distance between the slits,
- Z is the distance from the central maximum to the m-th dark spot,
- m is the order of the dark spot,
- L is the distance from the slits to the screen.
In this case, we have:
d = 0.0001 m, Z = 0.109 m, m = 8 (since we are counting 8 dark spots from the central maximum), L = 2.49 m.
Substituting these values into the formula, we get:
λ = (0.0001 m * 0.109 m) / (8 * 2.49 m)
Solving this equation gives us the wavelength in meters. To convert this to nanometers (nm), we multiply by 1x10^9 (since 1 m = 1x10^9 nm).
Let's calculate:
λ = (0.0001 * 0.109) / (8 * 2.49) * 1x10^9
After calculating, we get λ ≈ 549 nm.
So, the wavelength of the laser is approximately 549 nm.
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