Question

In Part 6.2.2, you will determine the wavelength of the laser by shining the laser beam on a "diffraction grating", a set of regularly spaced lines. Suppose the pattern is displayed on a screen a distance L from the grating and the spots are separated by s. If the screen is 11 m away, the spots are 4.5 cm apart, and the lines of the grating are separated by 0.5 mm, what is λ (mm)?

Answer 1

λ = 2042 nm

Step-by-step explanation:

given data

screen distance d = 11 m

spot s = 4.5 cm = 4.5 ×
`10^(-2)` m

separation L = 0.5 mm = 0.5 ×
`10^(-3)` m

to find out

what is λ

solution

we will find first angle between first max and central bright

that is tan θ = s/d

tan θ = 4.5 ×
`10^(-2)` / 11

θ = 0.234

and we know diffraction grating for max

L sinθ = mλ

here we know m = 1 so put all value and find λ

L sinθ = mλ

0.5 ×
`10^(-3)` sin(0.234) = 1 λ

λ = 2042.02 ×
`10^(-9)` m

λ = 2042 nm