Coherent and Incoherent Addition of Waves Video Lecture | Physics for JEE Main & Advanced

hello friends this video on wave optics
part 13 is brought to you by insane feel
calm no more fear from exam please make
sure that you have watched all the
videos still part 12 before going ahead
with part 13 now let us look at the
coherent and incoherent addition of
waves so how do we add waves coming from
coherent and incoherent sources so what
we will do it now in the last three
slides what we did we took some specific
values we took a scenario where path
difference is zero we took another
scenario where path difference is two
lambda we took yet another scenario
where path difference is minus two point
five lambda so now we will generalize
things let us say that we have two waves
first wave is given by y1 is equal to a
cos Omega T and the second wave is given
by a cos Omega T plus Phi where Phi is
some phase difference between the two
waves right and let us suppose that the
individual intensity of each of them is
I naught okay so the individual
intensity of each of them is I naught
which is proportional to a square right
that is the square of the amplitude so
what would be the resultant displacement
it would be nothing but vector addition
of y1 and y2 so this comes out to be a
cos Omega T plus a cos Omega T plus Phi
so this can be simplified using cos a
plus cos B what is the formula cos a
plus cos B it is two cos a plus B by 2
cos a minus V by 2 you must have studied
all these things in your trigonometry so
therefore this equation will become 2 a
cos Phi by 2 cos Omega T plus Phi by 2
so this is my resident displacement so
looking at this we can say that which is
the amplitude amplitude is this part
because normally it is in the form of a
cos Omega T so the cosine part is this
one so the remaining part has to be
amplitude so this is my amplitude part
so what would be the intensity intensity
is directly proportional to amplitude
square so we can say intensity is
directly proportional to for a square
cos square Phi by 2 so we can say that I
is equal to what is a square a square is
nothing but I naught so hence of for I
naught cos square Phi by 2 so if the two
waves have any phase difference Phi so
we can apply this for coherent as well
as in coherent waves because any
coherent waves also if we know the phase
difference between the two waves we can
calculate the resultant intensity at
some point alright so I hope you
understood how constructive destructive
overlap takes place and under what
condition constructive overlap happens
and under what condition destructive
overlap happens because these are the
basis of Young's double-slit experiment
if you understand all this then it will
be easier for you to understand the
Young's double-slit experiment so let us
quickly summarize whatever we have
studied so far you need summarize it
here so when we talk about constructive
overlap so constructive overlap takes
place when path difference is n lambda
and the phase difference that is Phi is
0 plus minus 2 pi plus minus 4 pi and so
on because these are the phases
corresponding to the path difference
lambda where as destructive interference
takes place when path difference is
equal to n plus 1 by 2 lambda I am the
file or the phase corresponding to this
is plus minus PI plus minus 3 PI plus
minus 5 5 and so on so these are the
conditions under which constructive and
destructive overlap takes place now
after this it is good to start to the
phenomenon of interference the
phenomenon of interference was explained
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