Answer:
In Young's double slit experiment, the fringe width is given by \[\beta =\frac{D\lambda }{d}\] (a) When the screen is moved away from the plane of the slits, the distance D increases. Hence fringe width \[\beta \] increases\[(\beta \propto D)\]. But the angular separation \[(=\lambda /d)\] of the triangles remains constant. (b) The decrease in wavelength \[\lambda \] decreases the fringe width\[\beta (\beta \propto \lambda )\]. Also the angular separation of fringes decreases. (c) As the separation d between the two slits increases, the fringe width \[\beta \] decreases\[(\beta \propto 1/d)\]. (d) Let s be the width of the source slit and S its distance from the plane of the two slits. For interference fringes to be distinctly seen, the condition \[\frac{s}{S}<\frac{\lambda }{d}\] should be satisfied, otherwise, the interference patterns produced by different parts of the source slit will overlap. The minima will not be totally dark and no fringe will be seen. So as the source slit is brought closer, the value of S decreases and the interference pattern becomes less and less sharp. When the source is brought very close so that the above condition gets violated, the fringes disappear. However, as long as the fringes are visible, the fringe width remains constant. (e) A broad source is equivalent to a large number of narrow sources placed close together. All such narrow sources produce their own interference patterns which overlap with each other and so the fringe pattern becomes less and less sharp. When the source slit is so wide that the condition \[\frac{s}{S}<\frac{\lambda }{d}\] is not satisfied, the interference pattern disappears. (f) The angular size of the central diffraction band due to each slit is about\[\frac{\lambda }{S'}'\] where S' is the width of each of the two slits. S' should be sufficiently small so that these bands are wide enough to overlap and thus produce interference. This means\[\frac{\lambda }{S'}>\frac{\lambda }{d},\] i.e., the width of each slit should be considerably smaller than the separation between the slits. When the slits are so wide that this condition is not satisfied, fringes are not seen. However, increase in the width of the slits does improve the brightness of the fringes. Thus, in practice, the two slits should be wide enough to allow sufficient light to pass through but narrow enough to cause enough diffraction from each slit to enable wavefronts from the two slits to overlap and interfere. (g) White light consists of colours from violet to red with wavelength from 4000 \[\overset{\text{o}}{\mathop{\text{A}}}\,\] to 7000 \[\overset{\text{o}}{\mathop{\text{A}}}\,\]. The interference patterns due to different component colours of white light overlap. At the centre of the screen, the path difference is zero for all such components. Therefore, the central fringe is white. Since the violet colour has the lowest \[\lambda \], the closest fringe on either side of the central white fringe is violet, while the farthest fringe is red. After a few fringes, the fringe pattern is lost due to large overlapping.
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