Superposition: (1) a double-slit, and

The idea

In the double-slit technique, coherent light passes through two narrow slits separated by a small distance a and falls on a screen a distance D away. Bright fringes occur where the path difference from the two slits is a whole number of wavelengths, and dark fringes where it is an odd number of half wavelengths. The fringe spacing x is measured between corresponding points on adjacent bright fringes, ideally by measuring across several fringes and dividing by the number of intervals. The wavelength follows from λ = ax/D. For example, if a = 0.25 mm, D = 2.00 m and ten fringe intervals span 48.0 mm, then x = 4.80 mm and λ = (0.25 × 10⁻³ m × 4.80 × 10⁻³ m) / 2.00 m = 6.0 × 10⁻⁷ m. The slits must be narrow enough to diffract light and close enough that a ≪ D.

What earns the marks

• Sets up two narrow, closely spaced slits illuminated by coherent monochromatic light.
• Measures the slit separation a and the perpendicular screen distance D.
• Measures the distance across several fringe intervals and divides by the number of intervals to find x.
• Applies λ = ax/D, converting all lengths to metres.
• Explains that bright fringes correspond to path differences of whole wavelengths and dark fringes to half-wavelength path differences.
• Identifies that the slits must be narrow enough to produce noticeable diffraction and close enough that a ≪ D.

Common mistakes and how to put them right

• Measuring the distance across n bright fringes and dividing by n rather than by the number of intervals n − 1.

  Put it right by counting intervals between fringes.

• Using a wide single slit instead of two narrow slits.

  Put it right by using a double slit so two coherent sources interfere.

• Assuming the central fringe is a dark fringe.

  Put it right by recognising the central point is a bright fringe because the path difference there is zero.

• Neglecting to darken the room, so the fringes are washed out by background light.

  Put it right by reducing ambient light or using a laser.

Exam tips

• Draw a clear ray diagram showing the two slits, the screen and the distances a, x and D.
• Measure across as many fringes as possible and divide by the number of intervals to reduce percentage uncertainty in x.
• Check that a ≪ D before applying λ = ax/D; if not, the small-angle approximation fails.
• State the colour or wavelength of the source, since fringe spacing depends on wavelength.