A helium-neon laser ( λ=633nm) illuminates a single slit and is observed on a screen 1.50m behind the slit. The distance between the first and second minima in the diffraction pattern is 4.75 mm.
What is the width (in mm) of the slit?
aren't there standard equations for this?
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To find the width of the slit, we can use the formula for the angular position of the minima in a single-slit diffraction pattern:
θ = λ / w
Where:
θ is the angular position of the minima
λ is the wavelength of the light
w is the width of the slit
In this case, we are given the distance between the first and second minima (4.75 mm), and we can assume that they are symmetrically located on either side of the central maximum. So we can consider the distance between the central maximum and the first minimum as half of the given distance.
Therefore, the distance between the central maximum and the first minimum (d) is:
d = 4.75 mm / 2 = 2.375 mm
Now, we need to calculate the angular position of the first minimum.
θ = λ / w
Since the distance between the slit and the screen is 1.50 m, we can use the small angle approximation, which states that for small angles the tangent of the angle is equal to the angle in radians:
tan(θ) = d / L
Where L is the distance between the slit and the screen.
θ = tan^(-1)(d / L)
θ = tan^(-1)(0.002375 m / 1.50 m)
Now we can calculate the width of the slit by rearranging the formula:
w = λ / tan(θ)
w = 633 nm / tan(θ)
Calculating θ:
θ = tan^(-1)(0.002375 / 1.50) ≈ 0.001593 radians
Now we can calculate the width of the slit:
w = 633 nm / tan(0.001593)
w ≈ 397.18 μm
Therefore, the width of the slit is approximately 397.18 μm or 0.39718 mm.