Laser light of wavelength 550 nm falls upon a diffraction grating. The slits are 25 micrometers apart and each have a
width of 2 micrometers. There is a screen 2 meters away from the diffraction grating, parallel to the grating.
A) At what angle does the m = 1 intensity peak occur?
To find the angle at which the m = 1 intensity peak occurs, we can use the formula for the angular position of the intensity peaks in a diffraction grating:
sinθ = mλ / d
Where θ is the angle, m is the order of the intensity peak, λ is the wavelength of the light, and d is the distance between the slits on the diffraction grating.
Given:
λ = 550 nm = 550 x 10^(-9) m
d = 25 μm = 25 x 10^(-6) m
m = 1
Substituting these values into the formula, we can find the angle:
sinθ = (1)(550 x 10^(-9) m) / (25 x 10^(-6) m)
Dividing these values gives:
sinθ = 0.022
Now, to find the angle θ, we can use the inverse sine function (sin^(-1)):
θ = sin^(-1)(0.022)
Using a scientific calculator, we find:
θ ≈ 1.26 degrees
Therefore, the m = 1 intensity peak occurs at an angle of approximately 1.26 degrees.
To calculate the angle at which the m = 1 intensity peak occurs, we can use the formula for the angle of diffraction:
sinθ = mλ / d
Where:
- θ is the angle of diffraction
- m is the order of the intensity peak
- λ is the wavelength of the light
- d is the distance between the slits on the grating
Given:
- λ = 550 nm = 550 × 10^(-9) meters
- d = 25 μm = 25 × 10^(-6) meters
- m = 1
Substituting the given values into the formula and solving for θ:
sinθ = (1)(550 × 10^(-9)) / (25 × 10^(-6))
sinθ = 0.022
Using the inverse sine function, we can find the angle θ:
θ = sin^(-1)(0.022)
θ ≈ 1.26°
Therefore, the m = 1 intensity peak occurs at an angle of approximately 1.26°.