#first minimum

Optical Phenomena and Applications

What is the angular position of the first minimum in a single-slit diffraction pattern if the slit width is \( 15.0 \, \

**Polarization requires transverse waves** because only transverse can have orientation perpendicular to propagation, longitudinal cannot be polarized, wave theory requires light transverse to explain polarization, polaroids transmit only component along pass-axis, unpolarized has random transverse orientations, after polaroid polarized. First minimum occurs at sin θ = (λ/a) . λ = 7.5 × 10⁻⁷ m , a = 1.5 × 10⁻⁵ m . sin θ = (7.5 × 10⁻⁷/1.5 × 10⁻⁵) = 0.05 , θ = sin⁻¹(0.05) ≈ 2.9° . Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ'

Ref: NCERT > Physics Book > Wave Optics > Optical Phenomena and Applications

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Wave Properties, Frequency and Energy Conservation

What is the angular position of the first minimum in a single-slit diffraction pattern if the slit width is \( 8.0 \, \m

**Intensity not depend on speed** when enters denser medium because intensity I ∝ n E₀²? Actually Poynting vector S = E×H, energy density u =½ ε E², for same amplitude E₀ intensity proportional to n, but amplitude changes at interface due to reflection, total energy conserved incident = reflected + transmitted, interference does not destroy energy, it redistributes. First minimum occurs at sin θ = (λ/a) . λ = 6.4 × 10⁻⁷ m , a = 8.0 × 10⁻⁶ m . sin θ = (6.4 × 10⁻⁷/8.0 × 10⁻⁶) = 0.08 , θ = sin⁻¹(0.08) ≈ 4.6° . Using Δ = d sinθ, y =

Ref: NCERT > Physics Book > Wave Optics > Wave Properties, Frequency and Energy Conservation

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Wavefront and Huygens Principle

What is the angular position of the first minimum in a single-slit diffraction pattern if the slit width is \( 10.0 \, \

**Huygens principle** predicts shape of wavefront after propagation, for point source close spherical, far plane, after reflection from plane mirror spherical wave becomes spherical with centre mirrored, plane wave remains plane but direction changes angle of incidence equals reflection, after passing through thin prism plane wavefront tilts due to different path. First minimum occurs at sin θ = (λ/a) . λ = 5.0 × 10⁻⁷ m , a = 1.0 × 10⁻⁵ m . sin θ = (5.0 × 10⁻⁷/1.0 × 10⁻⁵) = 0.05 , θ = sin⁻¹(0.05) ≈ 2.9° . Using Δ = d sinθ, y = n λ D/d, a sinθ = n

Ref: NCERT > Physics Book > Wave Optics > Wavefront and Huygens Principle

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Diffraction - Single-Slit and Central Maximum

In a diffraction experiment, if the slit width is \( 4.0 \, \mu\text{m} \) and the wavelength is \( 800 \, \text{nm} \),

**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. First minimum occurs at sin θ = (λ/a) . λ = 800 nm = 8.0 × 10⁻⁷ m , a = 4.0 μm = 4.0 × 10⁻⁶ m . sin θ = (8.0 × 10⁻⁷/4.0 × 10⁻⁶) = 0.2 , so θ = sin⁻¹(0.2) ≈ 11.5° . Using Δ = d

Ref: NCERT > Physics Book > Wave Optics > Diffraction - Single-Slit and Central Maximum

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