**Diffraction Grating and Spectral Components**White light is spread out into its spectral components by a diffraction grating. If the grating has **1980** lines per centimeter, at what angle does red light of wavelength 640 nm appear in the first-order spectrum? (Assume that the light is incident normally on the grating.)[Input box for answer] _____ °---**Explanation:**Diffraction gratings separate light into its component wavelengths by exploiting the wave nature of light. In this scenario, you are asked to calculate the angle at which red light appears within the first-order spectrum. You can find this angle using the grating equation:\[ d \sin(\theta) = m \lambda \]where:- $ d $ is the distance between the grating lines (1/1980 cm),- $ \theta $ is the angle of diffraction,- $ m $ is the order of the spectrum (first-order, $ m = 1 $ in this case),- $ \lambda $ is the wavelength of the light (640 nm).This exercise allows students to apply the principles of wave optics to determine how different wavelengths of light are diffracted through a grating.

This is a problem of Fraunhofer diffraction through a plane diffraction grating.

White light is spread out into its spectral components by a diffraction grating. If the grating has 1980 lines per centimeter, at what angle does red light of wavelength 640 nm appear in first-order spectrum? (Assume that the light is incident normally on the grating.)

White light is spread out into its spectral components by a diffraction grating. If the grating has 1980 lines per centimeter, at what angle does red light of wavelength 640 nm appear in first-order spectrum? (Assume that the light is incident normally on the grating.)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Diffraction of light

In physics, the term diffraction is defined as the bending of light around the corners of the obstacle. As a light ray passes by an aperture, it bends around the edges or through slits, it spreads out through a narrow opening. The diffracted light will produce fringes of bright and dark or colored bands which are labeled as a diffraction pattern.

Question

**Diffraction Grating and Spectral Components**

White light is spread out into its spectral components by a diffraction grating. If the grating has **1980** lines per centimeter, at what angle does red light of wavelength 640 nm appear in the first-order spectrum? (Assume that the light is incident normally on the grating.)

[Input box for answer] _____ °

---

**Explanation:**

Diffraction gratings separate light into its component wavelengths by exploiting the wave nature of light. In this scenario, you are asked to calculate the angle at which red light appears within the first-order spectrum. You can find this angle using the grating equation:

\[ d \sin(\theta) = m \lambda \]

where:
- $ d $ is the distance between the grating lines (1/1980 cm),
- $ \theta $ is the angle of diffraction,
- $ m $ is the order of the spectrum (first-order, $ m = 1 $ in this case),
- $ \lambda $ is the wavelength of the light (640 nm).

This exercise allows students to apply the principles of wave optics to determine how different wavelengths of light are diffracted through a grating.

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