question_answer

How will the angular separation and visibility of fringes in Young's double slit experiment change when (i) screen is moved away from the plane of the slits, and (ii) width of the source slit is increased?  

Answer:

                Fringe width, \[\beta =\frac{D\lambda }{d}\]                       Angular separation,  \[\theta =\frac{\beta }{D}=\frac{\lambda }{d}\] (i) When the screen is moved away from the slits, the distance D increases. Fringe width \[\beta \] increases but angular separation \[\theta (=\lambda /d)\]remains unchanged.                        (ii) The interference pattern becomes less and less sharp. When the source slit becomes so wide that the condition \[\frac{s}{S}<\frac{\lambda }{d}\]is not satisfied, the interference pattern disappears. But the angular width \[\theta (=\lambda /d)\] remains unchanged.