Fringes from Different Interfering Wavelengths Question : Coherent light with wa

Question

Fringes from Different Interfering Wavelengths

Question : Coherent light with wavelength 596nm passes through two very narrow slits, and the interference pattern is observed on a screen a distance of 3.00 m from the slits. The first-order bright fringe is a distance of 4.84 mm from the center of the central bright fringe.

For what wavelength of light will the first-order dark fringe (the first dark fringe next to a central maximum) be observed at this same point on the screen?

Express your answer in micrometers (not in nanometers).

= ________ ?m

Explanation / Answer

Here ,

for first order dark fringe to be at y = 4.84 mm

y = m*wavlength * D/d

4.84 *10^-3 = 0.5 * wavelength * 3/d

for first orde bright fringe

4.84 *10^-3 = 0.5 * 596 *10^-9 * 3/d

using both equations

wavelength = 2 * 596 nm = 1192 nm

the wavelength is 1.192 um

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