Question

The same diffraction grating is used with two different wave- lengths of light, $\lambda_{\mathrm{A}}$ and $\lambda_{\mathrm{B}}$ . The fourth-order principal maximum of light $\mathrm{A}$ exactly overlaps the third-order principal maximum of light B. Find the ratio $\lambda_{\mathrm{A}} / \lambda_{\mathrm{B}}$ .

Name: Problem 61, Chapter 27: Physics
Uploaded: 2020-05-15T03:15:44-08:00
Duration: 1 min 15 s
Channel: Farnaz Mohseni
Description: The same diffraction grating is used with two different wave- lengths of light, λA and λB . The fourth-order principal maximum of light A exactly overlaps the third-order principal maximum of light B. Find the ratio λA / λB .

   The same diffraction grating is used with two different wave-
lengths of light, $\lambda_{\mathrm{A}}$ and $\lambda_{\mathrm{B}}$ . The fourth-order principal maximum of light $\mathrm{A}$
exactly overlaps the third-order principal maximum of light B. Find the
ratio $\lambda_{\mathrm{A}} / \lambda_{\mathrm{B}}$ .

Physics

John D. Cutnell,… 9th Edition

Chapter 27, Problem 61

Instant Answer

Solved by Expert Farnaz Mohseni

05/15/2020

Step 1

Step 1: The diffraction grating equation is given by: \[d \sin \theta = m \lambda\] where $d$ is the grating spacing, $\theta$ is the angle of the principal maximum, $m$ is the order of the maximum, and $\lambda$ is the wavelength of the light. Show more…

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The same diffraction grating is used with two different wave- lengths of light, $\lambda_{\mathrm{A}}$ and $\lambda_{\mathrm{B}}$ . The fourth-order principal maximum of light $\mathrm{A}$ exactly overlaps the third-order principal maximum of light B. Find the ratio $\lambda_{\mathrm{A}} / \lambda_{\mathrm{B}}$ .

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Key Concepts

Diffraction Grating Equation

This equation, d sin ? = m?, relates the grating spacing (d), the angle (?) at which constructive interference occurs, the order of the maximum (m), and the wavelength (?) of light. It is fundamental for predicting the positions of bright fringes (principal maxima) when light passes through a diffraction grating.

Principal Maximum

Principal maxima are the bright regions observed in the diffraction pattern where light waves constructively interfere. These correspond to specific orders (m) in the grating equation, and their positions depend on the wavelength of the light and the characteristics of the grating.

Diffraction Order

The diffraction order (m) is an integer that designates the sequence of interference maxima. It represents the number of wavelengths by which paths of light differ. When different orders for different wavelengths overlap, it establishes a relation between the wavelengths, as given by equating m??? = m???.

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