Two slits are illuminated with light of wavelength 550 nm. At a point on the screen, the path difference is 1.65 µm. Which feature appears there?

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BlackTom AI · Accepted Answer

The problem presents a two-slit interference setup with a light wavelength of 550 nm and a given path difference of 1.65 μm at a point on the screen.

First, convert all quantities to consistent units: the path difference Δ = 1.65 μm = 1650 nm, and the wavelength λ = 550 nm.

Option a: Destructive, 2nd-order minimum. A destructive (dark) fringe occurs when Δ = (m + 1/2) λ for some integer m. If we test m = 1 for a second-order minimum, Δ would need to be Δ = (1 + 1/2) λ = 1.5 λ = 1.5 × 550 nm = 825 nm. This is not equal to the given 1650 nm, and in fact 1650 nm would correspond to Δ = (3 + 1/2) λ if anything, which is not an integer plus a half multiple for this wavelength. Therefore this option does not match the given path difference.

Option b: Constructive, 2nd-order maximum. Constructive maxima satisfy Δ = m λ for integer m. For a 2nd-order maximum, m = 2, so Δ should be 2λ = 1100 nm. The provided Δ is 1650 nm, which does not equal 1100 nm, so this is not a match.

Option c: Destructive, 3rd-order minimum. Destructive minima require Δ = (m + 1/2) λ. For a 3rd-order minimum, m = 3, so Δ should be (3 + 1/2) λ = 3.5 λ = 3.5 × 550 nm = 1925 nm. The given 1650 nm differs from 1925 nm, so this option is incorrect.

Option d: Constructive, 3rd-order maximum. A constructive maximum occurs when Δ = m λ. For a 3rd-order maximum, m = 3, giving Δ = 3λ = 3 × 550 nm = 1650 nm, which exactly matches the provided path difference. This alignment confirms a constructive interference feature of order three.

Putting these checks together, only the scenario where the path difference equals three times the wavelength exactly fits the given Δ, and that corresponds to a constructive maximum of order three. The other options fail because their required Δ values do not equal 1650 nm, either because they predict a dark fringe at a mismatch order or a different-order bright fringe that does not match the path difference.

SPH4U - Physics 12 (2025-26) - A

Two slits are illuminated with light of wavelength 550 nm. At a point on the screen, the path difference is 1.65 µm. Which feature appears there?

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