Two thin slits are 0.050 mm apart. Monochromatic light of wavelength 634 nm falls on the slits. If there is a screen 6.0 m away, how far apart are adjacent interference fringes?

Question

BlackTom AI · Accepted Answer

For double-slit interference the fringe spacing (distance between adjacent bright fringes) is y = λL / d, because for small angles sinθ ≈ tanθ ≈ y/L and the condition for adjacent maxima is Δx = λ.

1) Relevant knowledge points and concepts
- Double-slit interference formula: fringe spacing y = λL / d.
- Small-angle approximation (valid when screen distance L is much larger than slit separation d).
- Unit consistency: convert wavelength and slit separation to meters.

2) Complete reasoning process (step by step)
- Given: slit separation d = 0.050 mm, wavelength λ = 634 nm, screen distance L = 6.0 m.
- Convert units to meters:
  d = 0.050 mm = 0.050 × 10^(-3) m = 5.0 × 10^(-5) m
  λ = 634 nm = 634 × 10^(-9) m = 6.34 × 10^(-7) m
- Apply formula y = λL / d.

3) Calculations with intermediate steps
- Compute numerator λL:
  λL = (6.34 × 10^(-7) m) × (6.0 m) = 3.804 × 10^(-6) m
- Divide by d:
  y = (3.804 × 10^(-6) m) / (5.0 × 10^(-5) m) = 0.07608 m
- Convert to centimeters:
  0.07608 m × 100 cm/m = 7.608 cm ≈ 7.6 cm

4) Why the correct answer is correct
- The result directly follows from the standard double-slit fringe spacing formula with correct unit conversions. The small-angle approximation is appropriate because L (6.0 m) ≫ d (5.0×10^(-5) m).

5) Why the other choices are incorrect
- 0.76 mm = 0.00076 m is 100 times smaller than the correct 0.07608 m.
- 7.6 mm = 0.0076 m is 10 times smaller than the correct value.
- 76 cm = 0.76 m is 10 times larger than the correct value.
All three are off by factors of 10 or 100 due to misplaced decimal or unit conversion errors.

6) Conclusion
- The adjacent interference fringes are approximately 7.6 cm apart, which matches the provided correct answer: 7.6 cm.

Two thin slits are 0.050 mm apart. Monochromatic light of wavelength 634 nm falls on the slits. If there is a screen 6.0 m away, how far apart are adjacent interference fringes?单项选择题

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