Wave Optics

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A wavefront is a surface of constant phase on which all points oscillate in phase because they are at the same distance from the source. Example: When a stone is dropped in calm water, the circular ri

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Huygens' Principle states that each point on a wavefront is a source of secondary disturbances (wavelets) that spread out in all directions with the speed of the wave. The new wavefront at any later t

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Using Huygens' construction: sin i/sin r = v₁/v₂ = n₂/n₁ Snell's law: n₁ sin i = n₂ sin r This shows that when light bends toward the normal (r < i), the speed in the second medium is less than in the

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During refraction: v₁/λ₁ = v₂/λ₂ (frequency remains constant) When light enters a denser medium (v₁ > v₂), both wavelength and speed decrease, but frequency ν = v/λ remains the same. This is because f

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Critical angle (iₒ) is the angle of incidence in a denser medium for which the angle of refraction is 90°. Formula: sin iₒ = n₂/n₁ (where n₁ > n₂) For angles greater than iₒ, total internal reflection

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Coherent sources are sources that maintain a constant phase difference between them. They have the same frequency and their phase difference doesn't change with time. Coherent sources are necessary fo

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Constructive interference: Path difference = nλ (n = 0, 1, 2, 3...) Resultant intensity = 4I₀ Destructive interference: Path difference = (n + 1/2)λ (n = 0, 1, 2, 3...) Resultant intensity = 0

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For two waves: y₁ = a cos ωt and y₂ = a cos(ωt + φ) Resultant: y = 2a cos(φ/2) cos(ωt + φ/2) Resultant amplitude = 2a cos(φ/2) Intensity formula: I = 4I₀ cos²(φ/2) where I₀ is intensity from each sour