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Double-Slit Bright Fringes: Public Worked Question

A public interference question showing how wavelength, slit separation, and screen distance set the position of a double-slit bright fringe.

Question

In a Young's double-slit experiment, light of wavelength 500 nm500\,\text{nm} passes through slits separated by 0.10 mm0.10\,\text{mm}, and the pattern is viewed on a screen 2.0 m2.0\,\text{m} away. How far from the central maximum is the second-order (m=2m = 2) bright fringe?

  1. a.1.0 cm1.0\,\text{cm}
  2. b.2.0 cm2.0\,\text{cm}
  3. c.2.5 cm2.5\,\text{cm}
  4. d.4.0 cm4.0\,\text{cm}

Correct answer

B. 2.0 cm2.0\,\text{cm}

Full reasoning

  1. 1Bright fringes satisfy dsin⁡θ=mλd\sin\theta = m\lambda; for small angles this gives screen positions ym=mλL/dy_m = m\lambda L/d.
  2. 2Insert the values: y2=2(500×10−9 m)(2.0 m)/(1.0×10−4 m)y_2 = 2(500\times 10^{-9}\,\text{m})(2.0\,\text{m})/(1.0\times 10^{-4}\,\text{m}).
  3. 3The numerator is 2×500×10−9×2.0=2.0×10−6 m22 \times 500\times 10^{-9} \times 2.0 = 2.0\times 10^{-6}\,\text{m}^2; dividing by 1.0×10−4 m1.0\times 10^{-4}\,\text{m} gives 2.0×10−2 m2.0\times 10^{-2}\,\text{m}.
  4. 4The second-order bright fringe sits 2.0 cm2.0\,\text{cm} from the central maximum, and y≪Ly \ll L confirms the small-angle approximation.

Why each choice is right or wrong

Choice A

This is the first-order position λL/d\lambda L/d — the fringe spacing — obtained by using m=1m = 1 instead of m=2m = 2.

Choice B

Correct. y2=2λL/d=2(500×10−9)(2.0)/(1.0×10−4)=2.0×10−2 my_2 = 2\lambda L/d = 2(500\times 10^{-9})(2.0)/(1.0\times 10^{-4}) = 2.0\times 10^{-2}\,\text{m}.

Choice C

This applies the half-integer dark-fringe condition (m+12)λ(m + \tfrac{1}{2})\lambda with m=2m = 2, which locates a minimum rather than a maximum.

Choice D

This is the separation between the two second-order maxima on opposite sides of center, double the distance from the central maximum.

Related formula

Double-slit bright-fringe positions

ym=mλLdy_m = \frac{m\lambda L}{d}

Assumptions: The small-angle approximation holds (L is much larger than d and y). The two slits act as coherent point sources.

Related topic and practice

Interference and DiffractionSign in for current practice

This public explainer is separate from the protected practice bank. Current practice coverage varies.

Source and public-release record

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. University Physics Volume 3, Section 3.1: Young's Double-Slit Interference — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.

Review and maintenance

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Keiko Study editorial owner
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Technical reviewer pending
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Last source check
2026-08-07
Next scheduled review
2026-11-07

Recheck the cited OpenStax reference before each major GRE Physics preparation cycle.

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