#screen distance

Wavefront and Huygens Principle

In a double-slit experiment, if \( \lambda = 530 \, \text{nm} \), \( d = 0.15 \, \text{mm} \), and \( D = 1.8 \, \text{m

**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. Fringe width β = (λ D/d) . λ = 5.3 × 10⁻⁷ m , d = 1.5 × 10⁻⁴ m , D = 1.8 m . β = (5.3 × 10⁻⁷ × 1.8/1.5 × 10⁻⁴) = 6.36 × 10⁻³ m = 6.36 mm . Using Δ = d sinθ, y = n λ D/d,

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Diffraction - Single-Slit and Central Maximum

In a double-slit experiment, if \( \lambda = 450 \, \text{nm} \), \( d = 0.15 \, \text{mm} \), and \( D = 1.5 \, \text{m

**Single-slit diffraction** central maximum width W =2λ D/a, a slit width, D distance, angular width θ =2λ/a, first minimum at a sinθ = λ, fourth minimum a sinθ=4λ, sinθ=4λ/a, for a=5.0 μm λ=500 nm sinθ=4×0.5/5=0.4 θ≈23.6°, central maximum width increases when slit width reduced to half doubles width, when wavelength quadrupled width quadruples, when slit tripled width one-third. Fringe width β = (λ D/d) . λ = 4.5 × 10⁻⁷ m , d = 1.5 × 10⁻⁴ m , D = 1.5 m . β = (4.5 × 10⁻⁷ × 1.5/1.5 × 10⁻⁴) = 4.5 × 10⁻³ m = 4.5 mm . Using Δ =

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

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Interference - Double-Slit and Coherence

In a double-slit experiment, if the screen distance is doubled, what happens to the fringe width?

**Coherence** requires constant phase difference, two independent sources not coherent because phase random, prevents interference pattern, laser coherent, visibility of fringes determined by coherence, intensity and phase difference, coherent sources produce stable interference, incoherent intensity adds I = I₁+I₂ no interference, interference pattern distinguishes from diffraction. Fringe width β = (λ D/d) . If D is doubled, β doubles. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a cos(φ/2), calculation gives Doubles, illustrating interfer

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Interference - Double-Slit and Coherence

In a double-slit experiment, if the screen is moved closer to the slits, what happens to the fringe width?

**Coherence** requires constant phase difference, two independent sources not coherent because phase random, prevents interference pattern, laser coherent, visibility of fringes determined by coherence, intensity and phase difference, coherent sources produce stable interference, incoherent intensity adds I = I₁+I₂ no interference, interference pattern distinguishes from diffraction. Fringe width β = (λ D/d) . If D decreases, β decreases. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a cos(φ/2), calculation gives Decreases, illustrating inter

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Interference - Double-Slit and Coherence

What happens to the fringe width in a double-slit experiment if the distance between the slits and the screen is tripled

**Interference** occurs when two coherent waves superpose, path difference Δ = d sinθ, bright fringe when Δ = n λ, n integer, seventh bright Δ=7λ, dark fringe Δ = (2n-1)λ/2, second dark Δ=3λ/2, third dark 5λ/2, sixth dark 11λ/2, distance of bright fringe from central y = n λ D/d, D screen distance, d slit separation, for λ=650 nm d=0.5 mm D=1.0 m fifth dark? Actually dark y=(2n-1)λ D/(2d). Fringe width β = (λ D/d) . If D is tripled, β triples. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC

Ref: NCERT > Physics Book > Wave Optics > Interference - Double-Slit and Coherence

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Interference - Double-Slit and Coherence

What happens to the fringe width in a double-slit experiment if both the slit separation and screen distance are doubled

**Coherence** requires constant phase difference, two independent sources not coherent because phase random, prevents interference pattern, laser coherent, visibility of fringes determined by coherence, intensity and phase difference, coherent sources produce stable interference, incoherent intensity adds I = I₁+I₂ no interference, interference pattern distinguishes from diffraction. Fringe width β = (λ D/d) . If D and d are both doubled, β = (λ (2D)/2d) = (λ D/d) , so it remains the same. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a

Ref: NCERT > Physics Book > Wave Optics > Interference - Double-Slit and Coherence

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