Ask Question
12 April, 22:47

A lab technician uses laser light with a wavelength of 670 nm to test a diffraction grating. When the grating is 40.0 cm from the screen, the first-order maxima appear 6.00 cm from the center of the pattern. How many lines per millimeter does this grating have?

+3
Answers (1)
  1. 12 April, 23:07
    0
    N = 221.4 lines / mm

    Explanation:

    Given:

    - The wavelength of the source λ = 670 nm

    - Distance of the grating from screen B = 40.0 cm

    - The distance of first bright fringe from central order P = 6.0 cm

    Find:

    How many lines per millimeter does this grating have?

    Solution:

    - The derived results from Young's experiment that relates the order of bright fringes about the central order is given by:

    sin (Q) = n*λ*N

    Where,

    n is the order number 0, 1, 2, 3, ...

    λ is the wavelength of the light source

    Q is the angle of sweep respective fringe from central order

    N is the number of lines/mm the grating has

    - We will first compute the length along which the light travels for the first bright fringe:

    L^2 = P^2 + B^2

    L^2 = 40^2 + 6^2

    L^2 = 1636

    L = 40.45 cm

    - Now calculate the sin (Q) that the fringe makes with the central order:

    sin (Q) = P / L

    sin (Q) = 6 / 40.45

    - Now we will use the derived results:

    N = sin (Q) / n*λ

    Where, n = 1 - First order

    Plug values in N = (6 / 40.45) / (670 * 10^-6)

    N = 221.4 lines / mm
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A lab technician uses laser light with a wavelength of 670 nm to test a diffraction grating. When the grating is 40.0 cm from the screen, ...” in 📘 Physics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers