Light of wavelength 589 nm incident on a pair of slits...

Light of wavelength 589 nm incident on a pair of slits produces an interference pattern on a distant screen in which the separation between adjacent bright fringes at the center of the pattern is $0.530 \mathrm{cm} .$ A second light source, when incident on the same pair of slits, produces an interference pattern on the same screen with a separation of $0.640 \mathrm{cm}$ between adjacent bright fringes at the center of the pattern. What is the wavelength of the second source?

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Key Concepts

Young's Double-Slit Experiment

This concept involves the interference of light waves from two coherent sources separated by a distance (the slits). When these waves overlap on a distant screen, the resulting pattern of bright and dark fringes is evidence of constructive and destructive interference. The experiment demonstrates the wave nature of light and forms the basis for understanding various interference phenomena.

Fringe Spacing and Its Dependence on Wavelength

The separation between adjacent bright (or dark) fringes, often called the fringe spacing, is determined by the wavelength of the light, the distance between the slits, and the distance to the screen. The relationship is typically given by ?y = (?L)/d, implying that the fringe spacing is directly proportional to the wavelength when the slit separation and the distance to the screen remain constant. This proportionality allows for different wavelengths to be compared when observing changes in the interference pattern.

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