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In 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= 2.23 m from the slits. From one dark spot 7 further dark spots are counted and the distance is measured to be Z = 0.097 m.Calculate the wavelength λ of the laser.Express answer in nm (1x10-9m) to the nearest whole number.

Question

In 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= 2.23 m from the slits. From one dark spot 7 further dark spots are counted and the distance is measured to be Z = 0.097 m.Calculate the wavelength λ of the laser.Express answer in nm (1x10-9m) to the nearest whole number.

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Solution

To calculate the wavelength of the laser, we can use the formula for double-slit interference:

λ = (d * Z) / (m * L)

where:

  • λ is the wavelength of the laser,
  • d is the slit spacing,
  • Z is the distance from the first dark spot to the seventh dark spot,
  • m is the order of the dark spot (in this case, m = 7 because we are considering the seventh dark spot),
  • L is the distance from the slits to the wall.

Substituting the given values into the formula, we get:

λ = (0.0001 m * 0.097 m) / (7 * 2.23 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 * 0.097) / (7 * 2.23) * 1x10^9 nm

After calculating the above expression, we get the wavelength of the laser in nanometers.

This problem has been solved

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