Wave optics

The path difference of two coherent waves

$$\Delta_{d} = d2-d1$$

Δd - path difference

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The path difference of two coherent waves: interference maximum

$$\Delta_{d} = k\cdot \lambda$$

Δd - path difference
λ - wave length

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The path difference of two coherent waves: interference minimum

$$\Delta_{d} = \frac{(2\cdot k+1)\cdot \lambda}{2}$$

Δd - path difference
λ - wave length

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Thin-film interference: constructive (maximum)

$$2\cdot h\cdot n\cdot cos(\beta) = \frac{(2\cdot k+1)\cdot \lambda}{2}$$

h - film thickness
n - refraction index
β - refraction angle
λ - wave length

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Thin-film interference: destructive (minimum)

$$2\cdot h\cdot n\cdot cos(\beta) = k\cdot \lambda$$

h - film thickness
n - refraction index
β - refraction angle
λ - wave length

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Radii of Newton's rings

$$r = \sqrt {k\cdot R\cdot \lambda}$$

r - radius
R - radius of curvature of the lens
λ - wave length

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Radii of Newton's rings

$$r = \sqrt {\frac{(2\cdot k+1)\cdot R\cdot \lambda}{2}}$$

r - radius
R - radius of curvature of the lens
λ - wave length

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Light diffraction

$$l = \frac{d^{2}}{4\cdot \lambda}$$

l - distance from obstacle
d - obstacle size
λ - wave length

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Diffraction grating: maximums (bright stripes)

$$d\cdot sin(\phi) = k\cdot \lambda$$

d - lattice constant (parameter)
φ - diffraction angle
λ - wave length

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Diffraction grating: minimums (dark stripes)

$$d\cdot sin(\phi) = \frac{(2\cdot k+1)\cdot \lambda}{2}$$

d - lattice constant (parameter)
φ - diffraction angle
λ - wave length

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