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title: "Monochromatic light of wavelength \\(\\lambda\\) is incident normally on a barrier containing two identical parallel slits, each of width \\(a\\). The center-to-center separation between the two slits is \\(d = 3a\\). The resulting intensity pattern is observed on a distant viewing screen. Which of the following correctly states whether the third-order (\\(m = 3\\)) double-slit interference bright fringe is observed on the screen and provides the correct physical reasoning?"
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url: "https://nerd-notes.com/ubq/123148/"
date_modified: "2026-09-28T11:57:43+00:00"
---

# Monochromatic light of wavelength \(\lambda\) is incident normally on a barrier containing two identical parallel slits, each of width \(a\). The center-to-center separation between the two slits is \(d = 3a\). The resulting intensity pattern is observed on a distant viewing screen. Which of the following correctly states whether the third-order (\(m = 3\)) double-slit interference bright fringe is observed on the screen and provides the correct physical reasoning?

Monochromatic light of wavelength \(\lambda\) is incident normally on a barrier containing two identical parallel slits, each of width \(a\). The center-to-center separation between the two slits is \(d = 3a\). The resulting intensity pattern is observed on a distant viewing screen. Which of the following correctly states whether the third-order (\(m = 3\)) double-slit interference bright fringe is observed on the screen and provides the correct physical reasoning?

- **A.** The \(m = 3\) bright fringe is observed because the path-length difference between light from the centers of the two slits equals \(3\lambda\), satisfying the condition for constructive double-slit interference.
- **B.** The \(m = 3\) bright fringe is not observed because the angular position of this interference maximum coincides with the first single-slit diffraction minimum (\(a\sin\theta = \lambda\)), causing the intensity transmitted by each individual slit to be zero.
- **C.** The \(m = 3\) bright fringe is not observed because the path-length difference between the waves from the centers of the two slits is \(\dfrac{5}{2}\lambda\), producing complete destructive interference between the two slits.
- **D.** The \(m = 3\) bright fringe is observed because the central single-slit diffraction envelope extends out to an angle where \(a\sin\theta = 3\lambda\), fully enclosing all interference maxima up to \(m = 3\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123148/*