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@@ -193,52 +193,6 @@ $\delta = (m + \frac{1}{2}) \cdot \lambda$.
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| 10 | Finding the distance to the bright spots | $y_b = m\frac{L\lambda}{d}$ |
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| 11 | Finding the distance to the dark spots | $y_d = \left(m + \frac{1}{2}\right)\frac{L\lambda}{d}$ |
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1. Wavelength <br>
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$\lambda = 2\pi / k$, <br>
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where $\lambda$ = wavelength and k is a constant
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2. Path Difference <br>
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$\delta = r_2 - r_1$, <br>
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where $\delta$ is path difference and r is the length of path
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3. Square of Longer Source <br>
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$r_2^2 = r^2 + \left(\frac{d}{2}\right)^2 - 2r\left(\frac{d}{2}\right)\cos\left(\frac{\pi}{2} - \theta\right) = r^2 + \left(\frac{d}{2}\right)^2 + dr\sin\theta$, <br>
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where d is the distance from source to screen
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4. Square of Shorter Source <br>
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$r_1^2 = r^2 + \left(\frac{d}{2}\right)^2 - 2r\left(\frac{d}{2}\right)\cos\left(\frac{\pi}{2} + \theta\right) = r^2 + \left(\frac{d}{2}\right)^2 - dr\sin\theta$
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5. Derivation from 3 - 4 <br>
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$(r_2 - r_1)(r_2 + r_1) = 2dr\sin\theta$
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6. Small distance approximation <br>
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$\delta = r_2 - r_1 \approx d\sin\theta$
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7. Condition for constructive interference <br>
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$d\sin\theta = m\lambda, \quad m = 0, \pm1, \pm2, \pm3, \ldots \text{ (constructive interference)}$
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8. Condition for destructive interference <br>
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$d\sin\theta = \left(m + \frac{1}{2}\right)\lambda, \quad m = 0, \pm1, \pm2, \pm3, \ldots \text{ (destructive interference)}$
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9. Small Angle Approximation <br>
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$\sin\theta \approx \tan\theta = \frac{y}{L}$
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10. Finding the distance to the bright spots <br>
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$y_b = m\frac{L\lambda}{d}$
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11. Finding the distance to the dark spots <br>
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$y_d = \left(m + \frac{1}{2}\right)\frac{L\lambda}{d}$
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