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

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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

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$∆$ P = path difference (optical) = mλ = (µ – 1)² (x² + d²)

$\Rightarrow x^{2} = \frac{m^{2} λ^{2}}{{(µ - 1)}^{2}} - d^{2}$

On comparing x² = p²m²λ² – d²

$p^{2} = \frac{1}{{(µ - 1)}^{2}} = \frac{1}{{(4 / 3 - 1)}^{2}} = \frac{1}{{(1 / 3)}^{2}} = 9$

So, p = 3

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