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?

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