A light source, which emits two wavelengths $$\lambda_1 = 400 nm$$ and $$\lambda_2 = 600 nm$$, is used in a Young’s double slit experiment. If recorded fringe widths for $$\lambda_1$$ and $$\lambda_2$$ are $$\beta_1$$ and $$\beta_2$$ number of fringes for them within a distance yon one side of the central maximum are $$m_1$$ and $$m_2$$, respectively, then
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