• # question_answer (i) Why are coherent sources necessary to produce a sustained interference pattern? (ii) Describe briefly the formation of diffraction pattern on screen due to a narrow slit illuminated by a monochromatic light. Obtain the condition for angular width of secondary minima.

(i) Coherent sources produces light of constant phase difference and hence, permanent fringes pattern produced due to interference of light. (ii) A parallel beam of light with a plane wavefront is made to fall on a single slit UN. As width of the slit LN = a is of the order of wavelength of light, therefore diffraction occurs on passing through the slit. The wavelets from the single wavefront reach the centre C on the screen in same phase and hence, interfere constructively to give central maximum (bright fringe). The diffraction pattern obtained on the screen consists of a central bright band, having alternate dark and weak bright bands of decreasing intensity on both sides. Geometry of a single slit diffraction Consider a point P on the screen at which wavelets travelling in a direction, make an angle $\theta$ with MC. The wavelets from points L and N will have a path difference equal to NQ. From the right angled $\Delta LNQ,$ we have $NQ=LN\sin \theta$ or $NQ=a\sin \theta$ To establish the condition for secondary minima, the slit is divided into 2, 4, 6,... equal parts such that corresponding wavelets from successive regions interfere with path difference of $\lambda /2.$ Or for nth secondary minima, the slit can be divided into 2n equal parts. Hence, for nth secondary minima, Path difference $=\frac{a}{2}\sin \theta =\frac{\lambda }{2}$ or         $\sin {{\theta }_{n}}=\frac{n\lambda }{a}$       (where, n = 1,2,3,?)
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