Wave Properties, Frequency and Energy Conservation

Wave Properties, Frequency and Energy Conservation

What is the path difference for the fifth dark fringe in a double-slit experiment?

**Wave model predicts** light bends away from normal when entering rarer medium because speed increases, Snell's law n₁ sinθ₁ = n₂ sinθ₂, n₁>n₂ so sinθ₂>sinθ₁ θ₂>θ₁ away from normal, towards normal when denser, wavefront slows in denser, Huygens construction shows bending. Destructive interference occurs at Δ = (n + (1/2))λ . For the fifth dark fringe, n = 4 , Δ = (4 + (1/2))λ = (9λ/2) . 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 (9λ/2), illustrating interference, diffraction and polarization principles.

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Wave Properties, Frequency and Energy Conservation

Why does the interference pattern from two slits disappear if the slits are too far apart?

**Frequency of light** remains unchanged when refracts from air into water because frequency determined by source, energy E= h f conserved, speed decreases v= c/n, wavelength decreases λ'=v/f= λ/n, energy of wave proportional to amplitude² not speed, intensity I =½ c ε₀ E₀², energy not depend on speed directly, when speed decreases amplitude may change but energy conserved, interference redistributes energy, total energy same, bright regions gain from dark. Large slit separation reduces the overlap of wavefronts, disrupting the consistent path difference needed for stable interference. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ,

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Wave Properties, Frequency and Energy Conservation

In a double-slit experiment, if two wavelengths \( 600 \, \text{nm} \) and \( 400 \, \text{nm} \) are used, what is the

**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. Bright fringe position x_n = (n λ D/d) . Fringes coincide when n₁ λ₁ = n₂ λ₂ . 600 n₁ = 400 n₂ , n₂ = (3/2) n₁ . Smallest integers: n₁ = 2 , n₂ = 3 . x = (2 × 6.0 × 10⁻⁷ ×

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Wave Properties, Frequency and Energy Conservation

What causes the intensity of light to be zero at certain points in a diffraction pattern?

**Wave model predicts** light bends away from normal when entering rarer medium because speed increases, Snell's law n₁ sinθ₁ = n₂ sinθ₂, n₁>n₂ so sinθ₂>sinθ₁ θ₂>θ₁ away from normal, towards normal when denser, wavefront slows in denser, Huygens construction shows bending. Complete destructive interference occurs when secondary wavelets from different parts of the slit cancel each other out, resulting in zero intensity at minima. 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 Destructive interference, illustrating interference, diffraction and polarization principles.

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Wave Properties, Frequency and Energy Conservation

What is the distance of the fifth bright fringe from the central maximum in a double-slit experiment if \( \lambda = 490

**Frequency of light** remains unchanged when refracts from air into water because frequency determined by source, energy E= h f conserved, speed decreases v= c/n, wavelength decreases λ'=v/f= λ/n, energy of wave proportional to amplitude² not speed, intensity I =½ c ε₀ E₀², energy not depend on speed directly, when speed decreases amplitude may change but energy conserved, interference redistributes energy, total energy same, bright regions gain from dark. Bright fringe position x_n = (n λ D/d) . For the fifth bright fringe, n = 5 . λ = 4.9 × 10⁻⁷ m , d = 5.0 × 10⁻⁴ m , D = 1.0 m

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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 =

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Wave Properties, Frequency and Energy Conservation

What is the frequency of light with a wavelength of \( 600 \, \text{nm} \) in air, given the speed of light in air is \(

**Wave model predicts** light bends away from normal when entering rarer medium because speed increases, Snell's law n₁ sinθ₁ = n₂ sinθ₂, n₁>n₂ so sinθ₂>sinθ₁ θ₂>θ₁ away from normal, towards normal when denser, wavefront slows in denser, Huygens construction shows bending. Frequency nu = (c/λ) . λ = 600 nm = 6.0 × 10⁻⁷ m , c = 3.0 × 10⁸ m/s . nu = (3.0 × 10⁸/6.0 × 10⁻⁷) = 5.0 × 10¹⁴ Hz . 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

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Wave Properties, Frequency and Energy Conservation

What is the speed of light in a medium with refractive index 1.25, given the speed in vacuum is \( 3.0 \times 10^8 \, \t

**Frequency of light** remains unchanged when refracts from air into water because frequency determined by source, energy E= h f conserved, speed decreases v= c/n, wavelength decreases λ'=v/f= λ/n, energy of wave proportional to amplitude² not speed, intensity I =½ c ε₀ E₀², energy not depend on speed directly, when speed decreases amplitude may change but energy conserved, interference redistributes energy, total energy same, bright regions gain from dark. Speed in a medium v = (c/n) . Given n = 1.25 , c = 3.0 × 10⁸ m/s , v = (3.0 × 10⁸/1.25) = 2.4 × 10⁸ m/s . Using Δ = d sinθ,

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Wave Properties, Frequency and Energy Conservation

What is the shape of the wavefront after a plane wave passes through a thin prism?

**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. A plane wave passing through a prism gets tilted due to the varying thickness, resulting in a tilted plane wavefront. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' =

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Wave Properties, Frequency and Energy Conservation

What is the condition for the fifth minimum in a single-slit diffraction pattern?

**Wave model predicts** light bends away from normal when entering rarer medium because speed increases, Snell's law n₁ sinθ₁ = n₂ sinθ₂, n₁>n₂ so sinθ₂>sinθ₁ θ₂>θ₁ away from normal, towards normal when denser, wavefront slows in denser, Huygens construction shows bending. Minima occur at sin θ = (nλ/a) . For the fifth minimum, n = 5 , so θ = sin⁻¹((5λ/a)) . 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 θ = (5λ/a), illustrating interference, diffraction and polarization principles.

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Wave Properties, Frequency and Energy Conservation

What is the intensity at a point in a double-slit experiment where the phase difference is \( 3\pi \), if the maximum in

**Frequency of light** remains unchanged when refracts from air into water because frequency determined by source, energy E= h f conserved, speed decreases v= c/n, wavelength decreases λ'=v/f= λ/n, energy of wave proportional to amplitude² not speed, intensity I =½ c ε₀ E₀², energy not depend on speed directly, when speed decreases amplitude may change but energy conserved, interference redistributes energy, total energy same, bright regions gain from dark. Intensity I = 4I₀ cos²(Φ/2) . For Φ = 3π , I = 4I₀ cos²((3π/2)) = 4I₀ × 0 = 0 . Using Δ = d sinθ, y = n λ D/d, a sinθ = n

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Wave Properties, Frequency and Energy Conservation

What is the frequency of light with a wavelength of \( 510 \, \text{nm} \) in air, given the speed of light in air is \(

**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. Frequency nu = (c/λ) . λ = 5.1 × 10⁻⁷ m , c = 3.0 × 10⁸ m/s . nu = (3.0 × 10⁸/5.1 × 10⁻⁷) ≈ 5.88 × 10¹⁴ Hz . Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ,

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