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Question:

A Young's double slit interference arrangement with slits S1 and S2 is immersed in water (refractive index = 4/3) as shown in the figure. The positions of maxima on the surface of water are given by x² = p²m²λ² - d², where λ is the wavelength of light in air (refractive index = 1), 2d is the separation between the slits and m is an integer. The value of p is

Solution:

X1 = √X² + d²
X2 = μ√X² + d² = (4/3)√X² + d²
Path diff ΔX = (4/3)√X² + d² = nλ
X² + d² = 9n²λ² ⇒ p² = 9 ⇒ p = 3