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

Step-by-step solution

For n t h minima: ⇒ b sin θ = n λ ( λ is very small, so sin θ is very small, hence sin θ ≃ tan θ . ⇒ b tan θ = n λ ⇒ b y D = n λ ⇒ y n = n λ D b (Position of n t h minima) B → 1 st minima and A → 3 rd : y 3 = 3 λ D b , y 1 = λ D b ⇒ Δ y = y 3 - y 1 = 2 λ D 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