IB DP Physics: HL复习笔记9.4.2 Rayleigh Criterion Calculations

• The Rayleigh Criterion can be mathematically described by considering angular separation and single-slit diffraction
• Angular separation can be calculated using the equation:

• 
•  Where:
  • θ = angular separation (rad)
  • s = distance between the two sources (m)
  • d = distance between the sources and the observer (m)

Angular separation, θ, is equal to the separation, s, of two sources divided by the distance, d, between the sources and the observer

• In single slit diffraction, the first minimum occurs when the angle of diffraction is:

• • Wavelength of light sources, λ = 530 nm = 530 × 10−9 m
  • Student pupil diameter, b = 6.0 mm = 6.0 × 10−3 m
  • Distance from the helicopter light sources to the student's eye, d = 6.0 km = 6 × 103 m

• • Since the lights can just be resolved, this is Rayleigh's criterion
  • The equation needed is:

• • The approximate distance between the light sources on the helicopter, s = 65 cm

• • Wavelength of light sources, λ = 500 nm = 500 × 10-9 m
  • Student pupil diameter, b = 4.0 mm = 4.0 × 10-3 m
  • Distance of separation between headlights, s = 1.5 m

• • Since the answer will occur when Rayleigh’s criterion is met, the equation needed is: