Superposition: (f) Young double-slit experiment using visible light

The idea

Young's double-slit experiment demonstrates interference of visible light. Monochromatic light passes through a single slit to produce coherent waves, which then illuminate two closely spaced slits. The light from the two slits overlaps on a screen, producing a pattern of bright and dark fringes. Bright fringes occur where path difference is a whole number of wavelengths (nλ), and dark fringes where path difference is an odd number of half-wavelengths ((n + ½)λ). The fringe spacing x is given by x = λD/a, where λ is wavelength, D is distance from slits to screen, and a is slit separation.

For example: With λ = 6.0 × 10⁻⁷ m, D = 2.0 m and a = 0.50 mm, x = (6.0 × 10⁻⁷ × 2.0) / (0.50 × 10⁻³) = 2.4 × 10⁻³ m = 2.4 mm.

What earns the marks

• Young's double-slit experiment uses a single slit to produce coherent light that then illuminates two slits.
• The two slits act as coherent sources because light diffracts from the single slit and reaches both slits with a constant phase difference.
• Bright fringes occur where path difference is nλ; dark fringes occur where path difference is (n + ½)λ.
• The fringe spacing is given by x = λD/a, where D is the distance from the slits to the screen and a is the slit separation.
• The fringe spacing increases with wavelength and distance to the screen, and decreases with increasing slit separation.

Common mistakes and how to put them right

• Using two separate light sources instead of a single slit to illuminate the double slits.

  Put it right: The single slit ensures coherence, which is necessary for a stable interference pattern.

• Confusing the slit separation a with the distance D to the screen.

  Put it right: A is the small distance between the two slits, while D is the much larger distance from the slits to the screen.

• Forgetting to convert all lengths to metres before calculating.

  Put it right: Convert millimetres to metres, for example 0.50 mm = 0.50 × 10⁻³ m.

• Thinking that the central fringe is dark.

  Put it right: The central fringe is bright because the path difference is zero, giving constructive interference.

Exam tips

• When using x = λD/a, identify which quantity is being asked for and rearrange the equation before substituting numbers.
• Keep units consistent: convert all lengths to metres, and express wavelength in metres.
• If the question gives the distance across several fringes, divide by the number of fringe spacings to find x.
• Remember that the fringe spacing is measured between the centres of adjacent bright fringes or adjacent dark fringes.