Part 11 (B)Location of Maxima and minima:-
A dark fringe is defined as when there is no light or very small light then it appears dark. This is caused due to destructive interference on the either side of zero- order fringes. Light from one slit travels a distance that is ½ wavelengths longer than the distance traveled by light from the other slit.
Figure 3:- Shows the location of the dark fringes
Figure 4:- Shows the location of Central maxima
Dark Fringes:
d sin(θ)
(m + 1/2) λ where m = 0, 1, 2, 3, .n
If the value of m increases then number of dark and bright fringes goes on increases. The width of maxima goes on narrow because of neighboring closely located dark fringes. The total amount of light energy remains same; therefore narrower maxima require that each maximum reaches a correspondingly higher intensity.
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Figure 5:- Shows the location of dark and bright fringes for two, three and four slits
Intensity of light emitted by the slits increases as the width of the slit is increased. Thus, brighter fringes are formed at the screen on increasing the width of the slits. Zeroes of the pattern is located at the point where the value of the sin Θ =0. It is occur when the value of the Θ = m x π radian. It is relate with the bright fringes.
Π a sin Θ / λ
Or
a sin Θ = m λ
Figure 6:– Shows the graph of the dark fringes at the phase shift of 180 0
180 0 out of phase means when one value is at maximum at other is at minimum value. Destructive interference occurs when the maxima of two waves are at 180 0 out of phase then positive amplitude of one wave cancel the negative amplitude of other wave. We obtain zero resulting amplitude. This is point called minima.
Figure 7:- Shows the waveform of 180 0 phase shift.
