Two small openings in a ripple tank are 3.0 cm apart. The tank is 1.2 m long, and the wavelength is 0.60 cm. At what distance from the central maximum will the third bright fringe appear?

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BlackTom AI · Accepted Answer

Let’s parse the setup: two small openings separated by d = 3.0 cm = 0.03 m produce interference on a distant screen. The given wavelength is λ = 0.60 cm = 0.006 m, and the distance from the slits to the screen is L = 1.2 m. For a double-slit interference pattern, the bright fringes follow the condition y_m = m λ L / d, where m is the fringe order (m = 0 is the central maximum, m = 1 first bright, m = 2 second bright, etc.).

Option a: 0.36 m. If we test this distance with the formula, we get m = y d / (λ L) = 0.36 × 0.03 / (0.006 × 1.2) = 0.0108 / 0.0072 ≈ 1.5. Since m must be an integer for distinct bright fringes, this value is not physically consistent with a bright fringe order. This suggests 0.36 m is not the third bright fringe.

Option b: 0.60 m. Compute m = (0.60 × 0.03) / (0.006 × 1.2) = 0.018 / 0.0072 ≈ 2.5. Again, not an integer, so 0.60 m cannot correspond to a bright fringe of integer order, hence it is not the third bright fringe.

Option c: 0.72 m. Here m = (0.72 × 0.03) / (0.006 × 1.2) = 0.0216 / 0.0072 = 3. This yields exactly m = 3, which corresponds to the third bright fringe (central maximum is m = 0, first bright m = 1, second m = 2, third m = 3). Therefore this distance satisfies the interference condition for the third bright fringe.

Option d: 0.24 m. Then m = (0.24 × 0.03) / (0.006 × 1.2) = 0.0072 / 0.0072 = 1. This would place us at the first bright fringe, not the third, so this distance corresponds to m = 1 rather than m = 3.

In summary, evaluating each option against the bright-fringe condition shows that only 0.72 m yields an integer fringe order m = 3, matching the third bright fringe. The other distances fail to produce an integer order or correspond to a different fringe order, not the third bright one.

SPH4U - Physics 12 (2025-26) - A

Two small openings in a ripple tank are 3.0 cm apart. The tank is 1.2 m long, and the wavelength is 0.60 cm. At what distance from the central maximum will the third bright fringe appear?

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