A single slit is illuminated by light of wavelengths \( \lambda_{a} \) and \( \lambda_{b} \), ch...

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A single slit is illuminated by light of wavelengths \( \lambda_{a} \) and \( \lambda_{b} \), chosen so that the first diffraction minimum of the \( \lambda_{a} \) component coincides with the second minimum of the \( \lambda_{b} \) component. If \( \lambda_{b}=420 \mathrm{~nm} \), what is \( \lambda_{a} \) ? For what order number \( m_{b} \) (if any) does a minimum of the \( \lambda_{b} \) component coincide with the minimum of the \( \lambda_{a} \) component in the order number \( \quad m_{a}=2 \) and \( \quad m_{a}=3 \) ?
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