Halliday, Resnick & Walker — Diffraction: Problem 33

33 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. (a) If \(\lambda_b = 420 \text{ nm}\), 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 (b) \(m_a = 2\) and (c) \(m_a = 3\)?