Two narrow slits with a center-to-center distance of 0.48 mm are illuminated with coherent ligh

step 1 In this particular problem, it is given that for our double -slit experiments, G equals 0 .48 mi

Two narrow slits with a center-to-center distance of 0.48...

Two narrow slits with a center-to-center distance of $0.48 \mathrm{~mm}$ are illuminated with coherent light at normal incidence. The intensity of the light falling on a screen $5.0 \mathrm{~m}$ away is shown in the figure, where $x$ is the distance from the central maximum on the screen. (a) What would be the intensity of the light falling on the screen if only one slit were open? (b) Find the wavelength of the light.

Two narrow slits with a center-to-center distance of $0.48 \mathrm{~mm}$ are illuminated with coherent light at normal incidence. The intensity of the light falling on a screen $5.0 \mathrm{~m}$ away is shown in the figure, where $x$ is the distance from the central maximum on the screen.
(a) What would be the intensity of the light falling on the screen if only one slit were open? (b) Find the wavelength of the light.

Key Concepts

Double-Slit Interference

This concept explains how two coherent light sources, such as light passing through two narrow slits, combine to produce an interference pattern of alternating bright and dark fringes. The constructive interference from matching phases leads to brighter regions, while destructive interference from phase differences leads to darkness. This setup is a classic demonstration of the wave nature of light and is central to experiments like Young's double-slit experiment.

Single-Slit Diffraction

Even when light passes through a single narrow slit, it exhibits a diffraction pattern characterized by a central maximum and diminishing side lobes. This pattern arises due to the spread of wavefronts after passing through the aperture, and it forms an envelope that modulates the intensity distribution observed when multiple slits are used. Understanding single-slit diffraction is important for interpreting how the overall interference pattern is shaped.

Coherent Light Sources

Coherent light refers to light waves that maintain a constant phase relationship over time and space, which is essential for producing clear and stable interference patterns. In double-slit experiments, using coherent light ensures that the phase differences between the light waves emanating from the two slits are consistent, allowing predictable constructive and destructive interference.

Path Difference and Fringe Spacing

In interference experiments, the difference in distance traveled by light from each slit to a given point on the screen (the path difference) determines the phase difference between the waves, which in turn dictates the location of maxima and minima in the intensity pattern. This relationship is used to calculate the spacing between fringes and, when combined with geometric considerations, allows for the determination of the light’s wavelength.

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