During Young’s double-slit experiment, a student notices the pattern of bright and dark bands on the screen. To decrease the distance, [math: δx], between the adjacent dark bands, which one of the following actions should be taken?

Question

BlackTom AI · Accepted Answer

The fringe (band) spacing on the screen is given by β = λ D / d, so to reduce δx (the distance between adjacent dark bands) you must change the factors in that relation.

1. Relevant knowledge points and concepts
- Interference maxima/minima from two slits: path difference = mλ (bright) or (m + 1/2)λ (dark).
- Using small-angle approximations (sinθ ≈ tanθ ≈ y/D), the position of the m-th fringe on the screen is y_m = mλD/d.
- Fringe separation (distance between adjacent bright or adjacent dark fringes) is β = y_{m+1} − y_m = λD/d.

2. Step-by-step reasoning
- Start from path difference condition and geometry: d sinθ = mλ.
- For small θ, y ≈ D tanθ ≈ D sinθ, so y_m = D (mλ/d) = mλD/d.
- Subtract consecutive positions: β = (m+1)λD/d − mλD/d = λD/d.

3. Intermediate algebraic steps
- d sinθ = mλ → sinθ = mλ/d
- y = D tanθ ≈ D sinθ = D (mλ/d) → y_m = mλD/d
- β = y_{m+1} − y_m = λD/d

4. Why the correct answer is correct
- β is inversely proportional to slit separation d. Increasing d increases the denominator, decreasing β, so adjacent dark bands move closer together. That directly decreases δx.

5. Why the other options are incorrect
- (a) Increasing λ increases β (β ∝ λ), so bands get farther apart, not closer.
- (b) Decreasing frequency f increases wavelength (λ = c/f), which also increases β, so bands widen.
- (d) Increasing the distance D between slits and screen increases β (β ∝ D), so bands spread out.

Conclusion: Increasing the slit separation (option c) decreases the distance between adjacent dark bands. This matches the provided correct answer: c.

During Young’s double-slit experiment, a student notices the pattern of bright and dark bands on the screen. To decrease the distance, [math: δx], between the adjacent dark bands, which one of the following actions should be taken?单项选择题

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