(455) HL Multiple slit interference [IB Physics HL]

Diffraction Gratings and Multiple Slit Interference

  • Diffraction Grating: A structure with multiple openings allowing light to pass through.

    • D: Slit separation, measured in meters.

    • Lambda (λ): Wavelength of light, also measured in meters.

    • n: Order of interference (n = 0, 1, 2, 3, ...).

    • Theta (θ): Angle of light after passing through the grating.

Constructive Interference

  • Occurs when the path difference between two light beams equals nλ (multiple of wavelength).

  • Peaks in intensity arise due to constructive interference.

Interference Pattern with Monochromatic Light

  • Monochromatic light = light with a single wavelength.

  • Double Slit Interference: Modulated by single slit diffraction shapes.

    • Intensity pattern features broad peaks created by single slit modulation.

Finding Wavelength (λ) with a Diffraction Grating

  • Given: 600 lines per millimeter.

  • Light incident is normal to the grating with a second-order maximum seen at θ = 43°.

  • Key Equation: nλ = D sin θ

    • For second order (n = 2), λ = D sin(θ) / 2.

Calculating D (Slit Separation) from Given Information

  1. Convert lines per millimeter to lines per meter:

    • 600 lines/mm = 600,000 lines/m.

  2. Calculate D:

    • D = 1/N = 1/600,000 m = 1.67 x 10^-6 m.

Final Calculation of Wavelength (λ)

  • Substitute D into the equation:

  • λ = (1.67 x 10^-6 m) * sin(43°) / 2.

  • Resultant wavelength = 6.569 x 10^-7 m or 569 nm, rounded to three significant figures.