For a wavelength of 420 nm, a diffraction grating produces a bright fringe at an angle of 23°. For an unknown wavelength, the same grating produces a bright fringe at an angle of 35°. In both cases, the bright fringes are of the same order $ m $. What is the unknown wavelength?**Diagram Explanation:**The diagram shows a diffraction grating and the resulting diffraction pattern on a screen. Here's the breakdown:- **Diffraction Grating:** A vertical set of parallel lines or slits.- **Angles:** - $ \theta_1 $ corresponds to the angle for the known wavelength. - $ \theta_2 $ corresponds to the angle for the unknown wavelength.- **Fringes:** - **Central Bright Fringe:** Marked as $ m = 0 $, where no diffraction occurs. - **Bright Fringe $ m $ (known wavelength):** Shown at angles $ \theta_1 $ from the central fringe. - **Bright Fringe $ m $ (unknown wavelength):** Shown at angles $ \theta_2 $ from the central fringe.- **Arrangement:** Bright fringes for the known and unknown wavelengths are symmetrically arranged above and below the central fringe on the screen.The task is to determine the unknown wavelength given these angles and conditions.

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For a wavelength of 420 nm, a diffraction grating produces a bright fringe at an angle of 23°. For an unknown wavelength, the same grating produces a bright fringe at an angle of 35°. In both cases the bright fringes are of the same order m. What is the unknown wavelength? Number 133,30) Diffraction grating Units 02 Bright fringe m (unknown wavelength) Bright fringe m (known wavelength) Central bright fringe (m= 0) Bright fringe m (known wavelength) Bright fringe m (unknown wavelength) Screen

For a wavelength of 420 nm, a diffraction grating produces a bright fringe at an angle of 23°. For an unknown wavelength, the same grating produces a bright fringe at an angle of 35°. In both cases the bright fringes are of the same order m. What is the unknown wavelength? Number 133,30) Diffraction grating Units 02 Bright fringe m (unknown wavelength) Bright fringe m (known wavelength) Central bright fringe (m= 0) Bright fringe m (known wavelength) Bright fringe m (unknown wavelength) Screen

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

For a wavelength of 420 nm, a diffraction grating produces a bright fringe at an angle of 23°. For an unknown wavelength, the same grating produces a bright fringe at an angle of 35°. In both cases, the bright fringes are of the same order $ m $. What is the unknown wavelength?

**Diagram Explanation:**

The diagram shows a diffraction grating and the resulting diffraction pattern on a screen. Here's the breakdown:

- **Diffraction Grating:** A vertical set of parallel lines or slits.
- **Angles:**
- $ \theta_1 $ corresponds to the angle for the known wavelength.
- $ \theta_2 $ corresponds to the angle for the unknown wavelength.
- **Fringes:**
- **Central Bright Fringe:** Marked as $ m = 0 $, where no diffraction occurs.
- **Bright Fringe $ m $ (known wavelength):** Shown at angles $ \theta_1 $ from the central fringe.
- **Bright Fringe $ m $ (unknown wavelength):** Shown at angles $ \theta_2 $ from the central fringe.
- **Arrangement:** Bright fringes for the known and unknown wavelengths are symmetrically arranged above and below the central fringe on the screen.

The task is to determine the unknown wavelength given these angles and conditions.

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