IB · C · structured
Wave behaviour · Question 9
Wave behaviour · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 12
- Topics
- 1
- Answer
- Complete
Coherent light of wavelength 633 nm from a laser is incident normally on a pair of narrow parallel slits separated by 0.25 mm. An interference pattern is observed on a screen 2.40 m from the slits.
- (a)
Determine Determine the separation of adjacent bright fringes on the screen.
3 marks - (b)
Explain Explain, in terms of path difference, why a bright fringe appears at the centre of the pattern and why dark fringes appear either side of it.
3 marks - (c)
Suggest One of the two slits is now covered with a filter that halves the amplitude of the light passing through it. Suggest how the appearance of the pattern changes.
3 marks - (d)
Compare The double slit is replaced by a diffraction grating of 500 lines per millimetre, illuminated by the same laser. Compare the pattern produced with the double-slit pattern.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Determine Determine the separation of adjacent bright fringes on the screen.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
For small-angle double-slit interference, adjacent fringe separation is s = λD/d.
- 2
s = (633 × 10⁻⁹ × 2.40)/(0.25 × 10⁻³)
- 3
s = 6.1 × 10⁻³ m (6.1 mm)
(b)
Explain Explain, in terms of path difference, why a bright fringe appears at the centre of the pattern and why dark fringes appear either side of it.
State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.
- 1
at the centre the two paths are equal, so the path difference is zero and the waves arrive in phase and interfere constructively
- 2
moving away from the centre, the path difference grows
- 3
where it reaches half a wavelength the waves arrive antiphase and cancel, giving a dark fringe; where it reaches a whole wavelength they reinforce again
(c)
Suggest One of the two slits is now covered with a filter that halves the amplitude of the light passing through it. Suggest how the appearance of the pattern changes.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
the fringe separation is unchanged, because it depends only on λ, D and d
- 2
the dark fringes are no longer completely dark, because the two amplitudes no longer cancel exactly
- 3
so the contrast between bright and dark fringes is reduced, and the bright fringes are dimmer
(d)
Compare The double slit is replaced by a diffraction grating of 500 lines per millimetre, illuminated by the same laser. Compare the pattern produced with the double-slit pattern.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
the grating produces maxima that are much sharper and narrower, separated by wide dark regions, rather than broad fringes of gradually varying brightness
- 2
the maxima are much further apart, because the slit separation of 2.0 × 10⁻⁶ m is far smaller than 0.25 mm
- 3
each maximum is brighter, because light from many thousands of slits contributes to it rather than from only two
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