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Ch 35: Interference
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 15th EditionCh 35: InterferenceProblema 16
Capitolo 34, Problema 16

Coherent light of frequency 6.32 × 1014 Hz passes through two thin slits and falls on a screen 85.0 cm away. You observe that the third bright fringe occurs at ±3.11 cm on either side of the central bright fringe. (a) How far apart are the two slits? (b) At what distance from the central bright fringe will the third dark fringe occur?

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Identify the given quantities: frequency of light \(f = 6.32 \times 10^{14}\) Hz, distance to screen \(L = 85.0\) cm, and position of the third bright fringe \(y_3 = \pm 3.11\) cm. Convert all distances to meters for consistency in SI units.
Calculate the wavelength \(\lambda\) of the light using the relation between frequency and wavelength: \(\lambda = \frac{c}{f}\), where \(c = 3.00 \times 10^8\) m/s is the speed of light in vacuum.
Use the formula for the position of bright fringes in a double-slit interference pattern: \(y_m = \frac{m \lambda L}{d}\), where \(m\) is the fringe order (for the third bright fringe, \(m=3\)), \(L\) is the distance to the screen, and \(d\) is the slit separation. Rearrange this formula to solve for \(d\): \(d = \frac{m \lambda L}{y_m}\).
For part (b), recall that dark fringes occur at positions given by \(y_{dark} = \frac{(m + \frac{1}{2}) \lambda L}{d}\), where \(m\) is the dark fringe order starting from zero. Since we want the third dark fringe, set \(m=2\) (because the first dark fringe corresponds to \(m=0\)), and calculate \(y_{dark}\) using the previously found \(d\) and \(\lambda\).
Interpret the results: the slit separation \(d\) found in part (a) tells how far apart the two slits are, and the position \(y_{dark}\) from part (b) gives the distance from the central bright fringe to the third dark fringe on the screen.

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Double-Slit Interference

Double-slit interference occurs when coherent light passes through two closely spaced slits, producing a pattern of bright and dark fringes on a screen due to constructive and destructive interference of light waves. The position of bright fringes depends on the slit separation, wavelength, and distance to the screen.
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Young's Double Slit Experiment

Relationship Between Fringe Position and Wavelength

The position of bright fringes (maxima) in a double-slit experiment is given by y = (mλL)/d, where m is the fringe order, λ is the wavelength, L is the distance to the screen, and d is the slit separation. This formula links the physical setup to the observed interference pattern.
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Relationships Between Force, Field, Energy, Potential

Dark Fringe Position in Double-Slit Interference

Dark fringes (minima) occur where destructive interference happens, located at positions y = ((m + 0.5)λL)/d for integer m. These positions lie between the bright fringes and are essential for determining the full interference pattern on the screen.
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