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In Young's double slit experiment for what order does the wavelength of red light $(\lambda=780 \mathrm{~nm})$ coincide with $(\mathrm{m}+1)^{\text {th }}$ order of blue light $(\lambda=520 \mathrm{~nm})$
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We have
$$
\begin{aligned}
& \mathrm{y}=\frac{\mathrm{m} \lambda_1 \mathrm{D}}{\mathrm{d}}=\frac{780 \mathrm{~m} \lambda \mathrm{D}}{\mathrm{d}} \\
& \mathrm{y}=\frac{(\mathrm{m}+1) \lambda_2 \mathrm{D}}{\mathrm{d}}=\frac{520(\mathrm{~m}+1) \lambda \mathrm{D}}{\mathrm{d}} \\
& 780 \mathrm{~m}=520(\mathrm{~m}+1) \\
& 780 \mathrm{~m}=520 \mathrm{~m}+520 \\
& 260 \mathrm{~m}=520 \\
& \mathrm{~m}=2
\end{aligned}
$$
$$
\begin{aligned}
& \mathrm{y}=\frac{\mathrm{m} \lambda_1 \mathrm{D}}{\mathrm{d}}=\frac{780 \mathrm{~m} \lambda \mathrm{D}}{\mathrm{d}} \\
& \mathrm{y}=\frac{(\mathrm{m}+1) \lambda_2 \mathrm{D}}{\mathrm{d}}=\frac{520(\mathrm{~m}+1) \lambda \mathrm{D}}{\mathrm{d}} \\
& 780 \mathrm{~m}=520(\mathrm{~m}+1) \\
& 780 \mathrm{~m}=520 \mathrm{~m}+520 \\
& 260 \mathrm{~m}=520 \\
& \mathrm{~m}=2
\end{aligned}
$$
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