A lab technician uses laser light with a wavelength of 650 nm to test a diffraction grating. When the grating is 40.4 cm from the screen, the first-order maxima appear 6.09 cm from the center of the pattern. How many lines per millimeter does this grating have?

Number of lines per mm grating = 229

Explanation:

First of all, let's make use of the grating equation which is;

dsinθ=nλ,

where n=1 for a first order maximum.

Also tanθ=6.09/40.4, giving So, θ = tan^ (-1) 0.1507 = 8.572°.

So, d=λ/sinθ=

(650x10⁻⁹) / sin8.572°=

4.36x10⁻⁶m

Converting this to mm, we have d = 4.36x10⁻³mm

Now from formulas, number of lines (N) = 1/d

So, N = 1/d = 1 / (4.36x10⁻³) = 229.36 which is approximately 229 lines