In the Young's double slit experiment the intensity produced by each one of the individual slits is I₀. The distance between two slits is 2 mm. The distance of screen from slits is 10 m. The wavelength of light is 6000 Å. The intensity of light on the screen in front of one of the slits i $s ____.$
Options

Question

In the Young's double slit experiment the intensity produced by each one of the individual slits is I₀. The distance between two slits is 2 mm. The distance of screen from slits is 10 m. The wavelength of light is 6000 Å. The intensity of light on the screen in front of one of the slits i $s ____.$

Options

G1 Physics · Accepted Answer

For two coherent slits of equal individual intensity I₀, I = 4I₀ cos²(φ/2), where φ = 2πδ/λ. Take the origin at the midpoint of the two slits. The point directly in front of one slit is at y = d/2. For small angles, the path difference is δ = dy/D = d²/(2D). Given, d = 2×10⁻³ m, D = 10 m. Therefore, δ = (2×10⁻³)²/(2×10) = 2×10⁻⁷ m. The wavelength is λ = 6000 Å = 6×10⁻⁷ m. Hence, δ/λ = 1/3. Therefore, φ = 2π/3. Thus, I = 4I₀ cos²(π/3) = 4I₀(1/2)² = I₀. Correct option: B.