In a single slit diffraction pattern, a light of wavelength 6000 Å is used. The distance between the first and third minima in the diffraction pattern is found to be 3 mm when the screen in placed 50 cm away from slits. The width of the slit i s ______ × 10⁻⁴ m.
Physics · Wave Optics · diffraction of light
JEE Mains 2024 29 Jan Evening Shift

Question

In a single slit diffraction pattern, a light of wavelength 6000 Å is used. The distance between the first and third minima in the diffraction pattern is found to be 3 mm when the screen in placed 50 cm away from slits. The width of the slit i s ______ × 10⁻⁴ m.

Physics · Wave Optics · diffraction of light

JEE Mains 2024 29 Jan Evening Shift

G1 Physics · Accepted Answer

For nth minima b sinθ = nλ (λ is small so sin θ is small, hence sin θ ≃ tan θ) b tanθ = nλ b(yₙ/D) = nλ ⇒ yₙ = nλD/b (Position of nth minima) Image B → 1st minima, A → 3rd minima y₃ = 3λD/b, y₁ = λD/b Δy = y₃ – y₁ = 2λD/b 3 × 10⁻³ = [2 × 6000 × 10⁻¹⁰ × 0.5]/b b = [2 × 6000 × 10⁻¹⁰ × 0.5]/[3 × 10⁻³] b = 2 × 10⁻⁴ m x = 2