question_answer

In a Young's double slit experiment, the position of the first fringe coincides with \[{{S}_{1}}\] and \[{{S}_{2}}\] respectively. What is the wavelength of light?

Answer:

                As shown in Fig. the bright fringes \[{{B}_{1}}\] and \[{{B}_{2}}\] on either side of O coincide with \[{{S}_{1}}\,and\,{{S}_{2}}\]respectively. Clearly,                                - \[\beta =\frac{d}{2}\] As \[\beta =\frac{D\lambda }{d}\]            \[\therefore \]\[\frac{d}{2}=\frac{D\lambda }{d}\] or            \[\lambda =\frac{{{d}^{2}}}{2D}\].