In a double-slit experiment, the separation between the slits is d = 0.25 cm and the distance of the screen D = 100 cm from the slits. If the wavelength of light used is λ = 6 0 0 0 A ∘ and I 0 is the intensity of the central bright fringe, the intensity at a distance x = 4 × 10 − 5 m from central maximum is

Question

In a double-slit experiment, the separation between the slits is d = 0.25 cm and the distance of the screen D = 100 cm from the slits. If the wavelength of light used is λ = 6 0 0 0 A ∘ and I 0 is the intensity of the central bright fringe, the intensity at a distance x = 4 × 10 − 5 m from central maximum is, I 0, I 0 2, 3 I 0 4, I 0 3

MARKS App · Accepted Answer

Path difference = xd D ⇒ Path difference = 4 × 1 0 - 5 × 0.25 × 1 0 - 2 1 Path difference = 1 × 1 0 - 7 Phase difference = path diff. λ × 2 π ⇒ Phase difference = 1 × 1 0 - 7 6 × 1 0 - 7 × 2 π Phase difference = 2 π 6 ⇒ Phase difference = π 3 ⇒ ϕ = 6 0 ∘ I R = I 1 + I 2 + 2 I 1 I 2 cos 6 0 ∘ ⇒ I R = I + I + 2 I × 1 2 I R = 3 I ⇒ I R = 3 I 0 4

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