(i) In Young's double slit exoeriment, deduce the condition for (a) constructive,
and (b) destructive interference at a point on the screen. Draw a graph
showing variation of intensity in the interference pattern against position
'x' on the screen.
(ii) Compare the interference pattern observed in Young's double slit experiment
with single slit diffraction pattern, pointing out three distinguishing features.
(i) (1/2 mark)
Path difference =
For x,d <<D
so, (1/2 mark)
For constructive interference
For destructive interference
n=0, 1, 2....
Path Difference (1 mark)
(a) The Interference pattern has number of equally spaced bright and
dark bands, while in the diffraction pattern the width of the central
maximum is twice the width of other maxima. (1/2 mark)
(b) In Interference all bright fringes are of equal intensity, whereas
in the difraction pattern the intensity falls as order if maxima
increases. (1/2 mark)
(c) In Interference pattern, maxima occurs at an angle ,where
a is the slit width, whereas in diffraction pattern, at the same
angle, first minimum occurs. (Here 'a' is the size of the slit.) (1/2 mark)