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title: "Light containing two spectral lines of unknown wavelengths \\(\\lambda_1\\) and \\(\\lambda_2\\) (where \\(\\lambda_1 > \\lambda_2\\)) is incident normally on a diffraction grating with line spacing \\(d\\). A detector observes that the \\(m\\)th-order principal maximum of \\(\\lambda_1\\) occurs at the exact same diffraction angle \\(\\theta\\) as the \\((m+1)\\)th-order principal maximum of \\(\\lambda_2\\). Which of the following expressions represents the difference in wavelengths, \\(\\Delta \\lambda = \\lambda_1 – \\lambda_2\\)?"
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url: "https://nerd-notes.com/ubq/116617/"
date_modified: "2026-08-04T05:25:17+00:00"
---

# Light containing two spectral lines of unknown wavelengths \(\lambda_1\) and \(\lambda_2\) (where \(\lambda_1 > \lambda_2\)) is incident normally on a diffraction grating with line spacing \(d\). A detector observes that the \(m\)th-order principal maximum of \(\lambda_1\) occurs at the exact same diffraction angle \(\theta\) as the \((m+1)\)th-order principal maximum of \(\lambda_2\). Which of the following expressions represents the difference in wavelengths, \(\Delta \lambda = \lambda_1 – \lambda_2\)?

Light containing two spectral lines of unknown wavelengths \(\lambda_1\) and \(\lambda_2\) (where \(\lambda_1 > \lambda_2\)) is incident normally on a diffraction grating with line spacing \(d\). A detector observes that the \(m\)th-order principal maximum of \(\lambda_1\) occurs at the exact same diffraction angle \(\theta\) as the \((m+1)\)th-order principal maximum of \(\lambda_2\). Which of the following expressions represents the difference in wavelengths, \(\Delta \lambda = \lambda_1 - \lambda_2\)?

- **A.** \(\dfrac{d \sin\theta}{m}\)
- **B.** \(\dfrac{d \sin\theta}{m+1}\)
- **C.** \(\dfrac{d \sin\theta}{2m+1}\)
- **D.** \(\dfrac{d \sin\theta}{m(m+1)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116617/*