Question

A beam of light consisting of two wavelengths \(400\ \text{nm}\) and \(600\ \text{nm}\) is used to illuminate a single slit of width \(1\ \text{mm}\). Find the least distance of the point from the central maximum where the dark fringes due to both wavelengths coincide on the screen placed \(1.5\ \text{m}\) from the slit.

Hint:

For coincidence of dark fringes in single-slit diffraction, use \[ n_1\lambda_1=n_2\lambda_2. \] First find the smallest integral values of \(n_1\) and \(n_2\), and then substitute into \[ y=\frac{nD\lambda}{a} \] to obtain the position of the coincident minimum.

Answer 1