---
title: "A beam containing two monochromatic wavelengths of light, \\(\\lambda_1 = 480\\text{ nm}\\) and an unknown wavelength \\(\\lambda_2\\), is incident normally on a diffraction grating. On a distant viewing screen, the fourth-order (\\(m = 4\\)) principal maximum of wavelength \\(\\lambda_1\\) appears at the exact same diffraction angle \\(\\theta\\) as the third-order (\\(m = 3\\)) principal maximum of wavelength \\(\\lambda_2\\). What is the wavelength \\(\\lambda_2\\)?"
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url: "https://nerd-notes.com/ubq/123235/"
date_modified: "2026-09-28T11:57:59+00:00"
---

# A beam containing two monochromatic wavelengths of light, \(\lambda_1 = 480\text{ nm}\) and an unknown wavelength \(\lambda_2\), is incident normally on a diffraction grating. On a distant viewing screen, the fourth-order (\(m = 4\)) principal maximum of wavelength \(\lambda_1\) appears at the exact same diffraction angle \(\theta\) as the third-order (\(m = 3\)) principal maximum of wavelength \(\lambda_2\). What is the wavelength \(\lambda_2\)?

A beam containing two monochromatic wavelengths of light, \(\lambda_1 = 480\text{ nm}\) and an unknown wavelength \(\lambda_2\), is incident normally on a diffraction grating. On a distant viewing screen, the fourth-order (\(m = 4\)) principal maximum of wavelength \(\lambda_1\) appears at the exact same diffraction angle \(\theta\) as the third-order (\(m = 3\)) principal maximum of wavelength \(\lambda_2\). What is the wavelength \(\lambda_2\)?

![A horizontal schematic diagram of a diffraction grating setup. On the left, two parallel horizontal arrows labeled incident light point to the right toward a vertical segmented line representing a diffraction grating. A horizontal dash-dotted line extends from the center of the grating to the center of a vertical flat screen on the right, labeled \(\theta = 0\). A straight line extends from the center of the grating upward at an angle \(\theta\) to a point on the screen, where a small filled rectangle indicates an overlapping fringe labeled \(m = 4\text{ (}\lambda_1\text{)}\) and \(m = 3\text{ (}\lambda_2\text{)}\). An arc between the central horizontal line and the angled line is labeled \(\theta\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596679-oyXmS5.jpg)

- **A.** \(360\text{ nm}\)
- **B.** \(480\text{ nm}\)
- **C.** \(640\text{ nm}\)
- **D.** \(960\text{ nm}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123235/*