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In Young’s double slit experiment carried out with light of wavelength (λ) = 5000 Å, the distance between the slits is 0.2 mm and the screen is at 200 cm from the slits. The central maximum is at x = 0. The third maximum (taking the central maximum as zeroth maximum) will be at x equal to

  1. 1.67 cm
  2. 1.5 cm
  3. 0.5 cm
  4. 5.0 cm

Correct answer: 1.5 cm

Solution

The position of the nth maximum in Young's double-slit experiment is given by x = nλD/d, where n is the order of the maximum, λ is the wavelength, D is the distance between the slits and the screen, and d is the distance between the slits. Substituting n = 3, λ = 5000 Å = 5 × 10⁻⁷ m, D = 2 m, and d = 0.2 mm = 2 × 10⁻⁴ m, we get x = (3 × 5 × 10⁻⁷ × 2) / (2 × 10⁻⁴) = 1.5 cm.

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