a)Using Huygen's construction of secondary wavelets explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a monochromatic beam of light is incident normally.
b)Show that the angular width of the first diffraction fringe is half that of the central fringe
c)Explain why the maxima at centre becomes weaker and weaker with increasing 'n' in case of diffraction
Dear student,
(a)
We can regard the total contribution of the wavefront LN at some point P on the screen as the resultant of superposition of its wavelets like LM,MM2,M2N.They have to super impose taking into account their proper phase difference. Hence we get maxima and minima ie diffraction pattern on the screen.
(b)
Condition for the first minimum on the screen is
Angular width on the central fringe of the screen is
Angular width of the first diffraction fringe is
Hence the angular fringe of the central fringe is twice as that of angular width of the central fringe.
(c)The maxima becomes weaker and weaker with increasing n because the effective part of wave front contributing to the maxima becomes smaller and smaller with increasing n.
Regards.
(a)
We can regard the total contribution of the wavefront LN at some point P on the screen as the resultant of superposition of its wavelets like LM,MM2,M2N.They have to super impose taking into account their proper phase difference. Hence we get maxima and minima ie diffraction pattern on the screen.
(b)
Condition for the first minimum on the screen is
Angular width on the central fringe of the screen is
Angular width of the first diffraction fringe is
Hence the angular fringe of the central fringe is twice as that of angular width of the central fringe.
(c)The maxima becomes weaker and weaker with increasing n because the effective part of wave front contributing to the maxima becomes smaller and smaller with increasing n.
Regards.