a laser beam with wavelength 632.8nm is incident normal to the plane of a diffraction grating with a slit separation d=2000nm. if the diffraction pattern is viewed on a screen 1m from the grating, find the distance separating the first, second, and third maxima in the pattern.

To determine the distance separating the first, second, and third maxima in the diffraction pattern, we need to use the equation for the angle of diffraction for a diffraction grating:

sinθ = mλ / d

where:
θ is the angle of diffraction,
m is the order of the maximum,
λ is the wavelength of the incident light, and
d is the slit separation of the grating.

First, we need to calculate the angle of diffraction for each maximum.

For the first maximum (m = 1):
sinθ₁ = (1)(λ) / d

For the second maximum (m = 2):
sinθ₂ = (2)(λ) / d

For the third maximum (m = 3):
sinθ₃ = (3)(λ) / d

Now, we can find the distances between the maxima on the screen. The distance between two consecutive maxima is given by:

Δy = L tan(θ)

where:
Δy is the distance between two consecutive maxima on the screen, and
L is the distance between the diffraction grating and the screen.

Given that L = 1m, we can calculate the distances:

For the first maximum:
Δy₁ = L tan(θ₁)

For the second maximum:
Δy₂ = L tan(θ₂)

For the third maximum:
Δy₃ = L tan(θ₃)

Now, let's substitute the values and calculate the distances for each maximum.