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Question

What is the angular position of the fourth minimum in a single-slit diffraction pattern if the slit
width is \( 5.0 \, \mu\text{m} \) and the wavelength is \( 500 \, \text{nm} \)?

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Explanation

**Diffraction bending** property of light waves causes bending around corners, width of central maximum inversely proportional to slit width, intensity of secondary maxima decreases with order because less constructive interference, angular position of minima θ_n = n λ/a, n=±1,±2..., second minimum n=2, third n=3, condition for third secondary maximum approx a sinθ = (2n+1)λ/2. Minima occur at sin θ = (nλ/a) . For the fourth minimum, n = 4 . λ = 5.0 × 10⁻⁷ m , a = 5.0 × 10⁻⁶ m . sin θ = (4 × 5.0 × 10⁻⁷/5.0 × 10⁻⁶) = 0.4 , θ = sin⁻¹(0.4) ≈ 23.6° . Using Δ

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