Coherence and Young's Double-Slit Fringes · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Two slits that paint with light

Science · Waves, Light & Sound · ages 16-18
Name ______________________   Date ____________

  1. For initially in-phase coherent slit outputs with matching polarisation and no extra phase shifts, a whole-wavelength path difference gives constructive interference.

    Circle one:   True   False

  2. What describes two coherent waves over the observation time?

    • Same frequency and a fixed phase difference
    • Same intensity and a changing phase difference
    • Same wavelength and unrelated changing frequencies

  3. In the small-angle fringe-spacing formula w = lambda D/s, what does s represent?

    • Distance from the slits to the screen
    • Centre-to-centre separation of the slits
    • Distance between neighbouring screen fringes

  4. Near the centre of a distant screen, fringes are 0.003 m apart. Slit separation is 0.0004 m and screen distance is 2 m. Use lambda = ws/D. Give wavelength in metres.

    Answer: ______________

  5. The slit separation doubles while wavelength and screen distance stay fixed. Within the small-angle approximation, what happens to fringe spacing?

    • It becomes half as large
    • It becomes twice as large
    • It remains the same size

  6. Two coherent sinusoidal slit outputs start in phase and reach a screen point with equal amplitudes and matching polarisation. With no extra phase shifts, which path difference gives zero intensity?

    • A path difference of one whole wavelength
    • A path difference of half a wavelength
    • A path difference of two whole wavelengths

  7. Each slit is illuminated by a different ordinary independent bulb. Why is no stable interference fringe pattern expected in a steady screen measurement?

    • Each bulb supplies waves of exactly fixed relative phase
    • Independent bulbs prevent any light from reaching the screen
    • The relative phase changes and interference averages out

  8. A red laser is replaced by a blue laser in the same medium, with slit separation and screen distance fixed. Near the screen centre, how does fringe spacing change?

    • It decreases because wavelength decreases
    • It increases because wavelength decreases
    • It stays fixed because geometry stays fixed
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Two slits that paint with light W1-mt_mONvXhPmwq-s1

  1. True · A whole number of additional cycles preserves the starting phase relationship, so the fields reinforce.
  2. Same frequency and a fixed phase difference · Coherence requires a common frequency and a phase difference that remains fixed; the difference need not be zero.
  3. Centre-to-centre separation of the slits · s measures the separation of the slit centres. D measures screen distance and w measures fringe spacing.
  4. 6e-7 · lambda = 0.003 × 0.0004 / 2 = 0.0000006 m, equivalent to 600 nm.
  5. It becomes half as large · Since w = lambda D/s, doubling the denominator s halves w.
  6. A path difference of half a wavelength · Half a wavelength adds half a cycle, making the equal arriving fields antiphase so they cancel.
  7. The relative phase changes and interference averages out · The bulbs do not maintain a stable relative phase. Their interference contributions average out over the measurement time.
  8. It decreases because wavelength decreases · Blue has a shorter wavelength than red in the same medium. Since w is proportional to wavelength, the spacing decreases.
Worksheet · LightMySky