Conducting an experiment with a 534-nm wavelength green laser, a researcher notices a slight shift in the image generated and suspects the laser is unstable and switching between two closely spaced wavelengths, a phenomenon known as mode‑hopping. To determine if this is true, she decides to shine the laser on a double‑slit apparatus and look for changes in the pattern. Measuring to the first bright fringe on a screen 0.500 m away and using a slit separation of 80.0 μm, she measures a distance of 3.34 mm from the central maximum. When the laser shifts, so does the pattern, and she then measures the same fringe spacing to be 3.44 mm. What wavelength ? is the laser “hopping” to?

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A: Given,d=1.11 mm   =0.0011 mD=8.55 my=4.94 cm  =0.0494 mn=10 for tenth bright fring

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