question_answer

Give reason for each of the following observations : (i) The resultant intensity at any point on the screen varies between zero and four times the intensity due to one slit, in young's double slit experiment. (ii) A few coloured fringes, around a central white region, are observed on the screen, when the source of monochromatic light is replaced by white light in Young's double slit experiment. (iii) The intensity of light transmitted by a polariod is half the intensity of the light incident on it.

Answer:

                (i) The resultant intensity, at any point on the screen, is given by \[I=4{{I}_{0}}{{\cos }^{2}}\frac{\phi }{2}\]                                 For constructive interference:                                 \[\phi =0,2\pi ,4\pi \]and so on                                 \[\Rightarrow \]               \[I=0\]for minimum intensity.                                 For destructive interference:                                 \[\phi =\pi 3\pi ,5\pi \]and so on                                                 \[\Rightarrow \]               \[I=4{{I}_{0}}\]for maximum intensity. Thus, intensity varies between zero and four times the intensity, due to each slit, in Young's double slit experiment. (ii) The interference patterns due to different colours of white light overlap incoherently.  The central bright fringes for different colours are at the same position. Therefore the central fringe is white and the fringes closest, on either side of central white fringe, are red and the farthest will appear blue. After a few fringes no clear fringe pattern is seen. (iii) A polaroid consists of a long chain of molecules aligned in a particular direction. The electric vector (associated with the propagating light wave) along the direction of the aligned molecules get absorbed. Thus, if the light, from an ordinary source, passes through a polaroid, it is observed that its transmitted intensity gets reduced by half.