Monochromatic light passes through two narrow slits and...

Monochromatic light passes through two narrow slits and forms an interference pattern on a screen. (a) If the wavelength of light used increases, will the distance between the maxima (1) increase, (2) remain the same, or (3) decrease? Explain. (b) If the slit separation is $0.25 \mathrm{~mm}$ the screen is $1.5 \mathrm{~m}$ away from the slits, and light of wavelength $550 \mathrm{nm}$ is used, what is the distance from the center of the central maximum to the center of the third-order maximum? (c) What if the wavelength is $680 \mathrm{nm}$ ?

Key Concepts

Double-Slit Interference

Double-slit interference refers to the phenomenon where coherent light passing through two narrow, closely spaced slits produces an interference pattern on a screen with alternating bright and dark fringes. The bright fringes (maxima) result from constructive interference, where the path difference between light from the two slits is an integer multiple of the light's wavelength.

Fringe Spacing

Fringe spacing is the distance between adjacent bright (or dark) fringes on the interference pattern. It is determined by the wavelength of the light, the separation between the slits, and the distance from the slits to the screen. Typically, using the small-angle approximation, the fringe spacing is proportional to the wavelength and the distance to the screen, and inversely proportional to the slit separation.

Wavelength Dependence

The wavelength of the light is directly proportional to the fringe spacing. This means that if the wavelength increases, the distance between the adjacent maxima increases as well. This dependency is a key aspect of the interference pattern produced by a double-slit arrangement.

Order of Maximum

Each bright fringe in the interference pattern is referred to as an order maximum. The central maximum is considered the zeroth order, and each subsequent maximum is labeled with an integer (first order, second order, etc.). The position of the m-th order maximum is related to both the wavelength and the geometry of the setup, and it can be calculated using the relation that involves the integer order, wavelength, and the distance between the slits.

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