Single-Slit Diffraction and the Limit of Resolution · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Single-slit diffraction and aperture resolution

Science · Waves, Light & Sound · ages 17-18
Name ______________________   Date ____________

  1. Red and violet light in the same medium use the same slit and far-field screen geometry. Which has the broader central maximum?

    • Violet, because shorter wavelengths spread more
    • Red, because longer wavelengths spread more
    • Both, because wavelength does not affect spreading

  2. In small-angle far-field diffraction from a uniformly illuminated slit, the slit narrows but stays much wider than the wavelength. Wavelength and screen distance stay fixed. What happens to the width between the first minima?

    • It grows wider
    • It grows narrower
    • It stays unchanged

  3. A narrow, uniformly illuminated single slit gives a sharp geometrical stripe rather than a diffraction pattern in the far field.

    Circle one:   True   False

  4. At fixed wavelength, why does a larger circular telescope aperture improve ideal diffraction-limited angular resolution?

    • It increases the blur and reduces collected light
    • It narrows each diffraction pattern's central blur
    • It widens each pattern and merges nearby point images

  5. Two identical finite slits are coherently illuminated and observed near a distant screen's centre. Which describes their interference spacing and brightness?

    • Equal spacing requires every fringe to have equal brightness
    • Spacing is approximately equal; an envelope varies brightness
    • Varying brightness means the interference spacing is irregular

  6. Within the small-angle single-slit approximation, wavelength doubles while slit width and screen distance stay fixed. How does central width W change?

    • W remains unchanged because slit width is fixed
    • W halves because wavelength is in the denominator
    • W doubles because it is proportional to wavelength

  7. Two equally bright stars are separated by 0.8 times a telescope's Rayleigh limit. Diffraction alone limits resolution. Its circular aperture diameter doubles at fixed wavelength. What does the criterion predict?

    • They satisfy the new Rayleigh criterion
    • They remain below the new Rayleigh criterion
    • They are exactly at the new Rayleigh limit

  8. At fixed screen distance and small angles, Nadia halves both wavelength and slit width. She predicts central width doubles. What does W proportional to lambda/a predict?

    • It doubles: slit width alone sets the width
    • It stays unchanged: both factors halve
    • It halves: wavelength alone sets the width
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Answer key

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Single-slit diffraction and aperture resolution W1-mt_qiG0fGadBU-s1

  1. Red, because longer wavelengths spread more · Red has the longer wavelength in the same medium, giving a broader central maximum with the slit and geometry fixed.
  2. It grows wider · The first minima exist in the stated regime. W is approximately 2 lambda D/a, so reducing a with lambda and D fixed increases W.
  3. False · The wavefront contributions interfere, producing a broad central maximum rather than the slit's geometrical shadow.
  4. It narrows each diffraction pattern's central blur · A larger aperture narrows each point's diffraction blur and lowers the Rayleigh threshold. Other sources of blur may still limit a real instrument.
  5. Spacing is approximately equal; an envelope varies brightness · Near the centre, interference fringes have approximately equal spacing, while each slit's diffraction envelope changes their brightness.
  6. W doubles because it is proportional to wavelength · W is approximately 2 lambda D/a. With D and a fixed, doubling lambda doubles W.
  7. They satisfy the new Rayleigh criterion · Doubling aperture diameter halves the threshold. The unchanged star separation is 0.8 old-limit units, greater than the new threshold of 0.5.
  8. It stays unchanged: both factors halve · The width factor is the wavelength factor divided by the slit-width factor: 0.5/0.5 = 1.
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