Question

Light of wavelength λ = 518 nm passes through a single slit of width w = 3.85 μm and illuminates a screen l = 1.4 m away. what is the maximum number of dark fringes of light could this setup produce on the screen?

Answer 1

The maximum number of dark fringes that the setup can produce is 7, determined by the integer part of the width of the slit divided by the wavelength.

Step-by-step explanation:

The student is asking about the diffraction pattern produced by light passing through a single slit and hitting a distant screen. Specifically, they want to know the maximum number of dark fringes that could be produced. To find this, we use the single-slit diffraction formula: d sin(θ) = mλ, where d is the width of the slit, θ is the angle of the minima, λ is the wavelength, and m is the order number of the dark fringe.

The maximum value of sin(θ) is 1, which occurs at θ = 90°. So we set sin(θ) to 1 and solve for m to obtain the maximum order number of dark fringes that the setup can produce: m = d/λ. Substituting the given values:

m = (3.85 × 10-6 m) / (518 × 10-9 m)
m ≈ 7.44

Since m must be an integer, the maximum number of dark fringes on the screen will be the integer part of m, which is 7 dark fringes.