In Fraunhofer diffraction pattern, slit width is 0.3 mm and screen is at 1.5 m away from the lens. If wavelength of light used is 4500 Å , then the distance between the first minimum on either side of the central maximum is [ is small and measured in radian.]

Step-by-step solution

The angular position ₁ of the first diffraction minimum is given by a ₁ = , where a = 0.3 10⁻³ m and = 4.5 10⁻⁷ m. Using the small-angle approximation ₁ ₁ , this simplifies to ₁ = /a . The linear distance from the central maximum to the first minimum is then y₁ = D ₁ = D /a , with D = 1.5 m. The separation between the first minima on either side is 2y₁ = 2D /a . Substituting the values: 2 1.5 4.5 10⁻⁷ 0.3 10⁻³ = 45 10⁻⁴ = 4.5 10⁻³ m. The distance is 4.5 mm , corresponding to option D.