Calculating the Width of a Single Slit in Diffraction Pattern

What is the width (in mm) of the slit if a helium-neon laser (λ = 633 nm) illuminates a single slit and the distance between the first and second minima in the diffraction pattern is 4.75 mm?

Calculating the Width of the Slit

To find the width of the slit in millimeters, we can use the formula for the single-slit diffraction pattern:

w = (λ * L) / D

where:

  • w is the width of the slit
  • λ is the wavelength of the laser light (633 nm)
  • L is the distance between the slit and the screen (1.90 m or 1900 mm)
  • D is the distance between adjacent minima in the diffraction pattern (4.75 mm)

First, we need to convert the given values to the appropriate units. The wavelength of the laser light is 633 nm, which is already in nanometers. The distance between the first and second minima is 4.75 mm, which is in millimeters. The distance between the slit and the screen is 1.90 m, which needs to be converted to millimeters:

L = 1.90 m * 1000 mm/m = 1900 mm

Now we can substitute the values into the formula to find the width of the slit:

w = (633 nm * 1900 mm) / 4.75 mm

Therefore, the width of the slit is approximately 2532 nanometers or 2.532 micrometers.

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