The distance between the two slits in Young's experiment is 0.2 mm. If the wavelength of the light used is 5000 A, the angular position of the fifth dark fringe from the central bright fringe is rad.

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(3) 0.011. Given: d = 0.2 mm = 2×10⁻⁴ m, λ = 5000 A = 5×10⁻⁷ m, and the fifth dark fringe. Idea: a dark fringe falls where the two paths differ by an odd number of half wavelengths, d sin θ = (2n-1)λ/2. For the fifth dark fringe n = 5, so the odd multiple is 2(5) - 1 = 9. sin θ = (9λ)/(2d) = (9 × 5×10⁻⁷)/(2 × 2×10⁻⁴) = (4.5×10⁻⁶)/(4×10⁻⁴). sin θ = 0.01125, and an angle this small is equal to its own sine to within a fraction of a percent, so θ ≈ 0.011 rad. The fifth dark fringe sits at about 0.011 rad from the centre.

The distance between the two slits in Young's experiment is 0.2 mm. If the wavelength of the light used is 5000 A, the angular position of the fifth dark fringe from the central bright fringe is ________ rad.

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