AS Daily A Level Physics question
A Young's double-slit experiment is performed in a vacuum, producing an interference pattern with a fringe spacing of 4.0 mm. The entire apparatus is then submerged in a transparent liquid with a refractive index of 1.6. The geometry of the setup (slit separation and distance to screen) remains unchanged. Which statement best describes the new fringe spacing and the physical reason for the change?
Answer
The correct answer is C.
Correct: C — 2.5 mm, because the wavelength of the light is shorter in the liquid than in a vacuum. The fringe spacing, w, is directly proportional to the wavelength, λ. When light enters a medium with refractive index n, its speed decreases, and since its frequency remains constant, its wavelength must also decrease according to λ_liquid = λ_vacuum / n. Therefore, the new fringe spacing is w_liquid = w_vacuum / n = 4.0 mm / 1.6 = 2.5 mm. A is incorrect because fringe spacing is inversely proportional to the refractive index, not directly proportional, leading to an incorrect calculation of 4.0 * 1.6 = 6.4 mm. B is incorrect because although the frequency does remain constant, the fringe spacing depends on wavelength, which changes when the medium changes. D is incorrect because the phase difference for a given path difference is inversely proportional to wavelength (Δφ = 2πΔx/λ); since the wavelength decreases, the phase difference for any point off the central axis actually increases, it does not reduce.