**Diffraction Grating and Visible Spectrum Analysis**---Intense white light is incident on a diffraction grating that has **464 lines/mm**.**(a)** What is the highest order in which the complete visible spectrum can be seen with this grating? (Enter 1 for first order, 2 for second order, etc.)[Text Box for Answer]**(b)** What is the angular separation between the violet edge (400 nm) and the red edge (700 nm) of the first order spectrum produced by the grating?[Text Box for Answer] °---### ExplanationThis problem involves determining the highest order and angular separation for light passing through a diffraction grating. A diffraction grating's ability to separate different wavelengths depends on its line density, measured in lines per millimeter.1. **Highest Order Calculation:** - The highest order refers to the maximum number at which the complete visible spectrum can be observed.2. **Angular Separation:** - This is the angle between the violet and red edges of the visible spectrum for a given order. It helps in understanding how well the grating separates different wavelengths.Understanding these concepts is crucial for applications in spectroscopy and optical analysis.

(a) The grid separation will be 1mm/464, the maximum viewing angle will be 90° and wavelength will be 700nm. The highest order that can be completely seen is given by, m=dsinθλ Here, d is the grid separation, θ is the viewing angle and λ is the wavelength. Substituting the values, m=1 mm/464×1 m103 mmsin90.0°700×10-9 m=3.08 Therefore, the highest order that can be observed is 3.(b) The formula to calculate the angular separation is given by, Δθ=sin-1mλrd-sin-1mλvd Here, λr is the wavelength of red light and λv is the wavelength of violet light. Substituting, Δθ=sin-11700×10-9 m1 mm/464×1 m103 mm-sin-11400×10-9 m1 mm/464×1 m103 mm=18.953°-10.696°=8.257°

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Intense white light is incident on a diffraction grating that has 464 lines/mm. (a) What is the highest order in which the complete visible spectrum can be seen with this grating? (Enter 1 for first order, 2 for second order, etc.) (b) What is the angular separation between the violet edge (400 nm) and the red edge (700 nm) of the first order spectrum produced by the grating?

Intense white light is incident on a diffraction grating that has 464 lines/mm. (a) What is the highest order in which the complete visible spectrum can be seen with this grating? (Enter 1 for first order, 2 for second order, etc.) (b) What is the angular separation between the violet edge (400 nm) and the red edge (700 nm) of the first order spectrum produced by 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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