Fringe Pattern (Part - 16 ) - Wave Optics, Physics, Class 12 Video Lecture

hello friends this video on wave optics
part 16 is brought to you by exam comm
no more fear from exam please make sure
that you have watched all the videos
till patch 15 before going ahead with
part 16 so now with the help of this
path difference let us study the fringe
pattern in detail what is the fringe
pattern fringe pattern is nothing but
the alternate dark and bright regions
which are obtained on the screen that is
known as the fringe pattern and each
dark or bright band is known as a fringe
hey this is just our terminology so what
a fringes or at any dark and bright
banks are known as fringes and this
pattern is known as fringe pattern so
now we are going to study about the
bright bands we want to know the
position of the bright bands so bright
bands will be formed as a result of
constructive interference and these
bright bands are the positions of
maximum intensity because constructive
interference all these results in
maximum intensity right now wait what
will what is the condition for maximum
intensity the condition for constructive
interference or maximum intensity
whatever you call it is that the path
difference should be integral multiple
of lambda right and what is the path
difference that we calculated in the
previous slide
it was XD divided by capital T is equal
to n lambda so X is equal to n lambda T
divided by D so this X represents the
position of a net right bank let us use
a subscript n so that it becomes easy so
this denotes the position of a net
bright Bank so this is how we can
calculate the position of a bright line
let's suppose if I tell you that L is in
Alvin Young's double-slit experiment we
have you used light or
wavelength so-and-so you tell me at word
position exactly the 10th bright band
will be fun so you can calculate it
using this expression because you know
tenth right back that means n is even
then write lambda is already mentioned
in the problem and capital D and small D
will be mentioned in the apparatus right
that what is the arrangement that has to
be mentioned so this is how we can
actually the position of the Emeth bribe
bank right when i talk about the when n
is equal to here if n is equal to 0 n is
equal to 0 represents the central bright
man this is the central bright bank so
this corresponds to n is equal to 0 when
I talk about the first right band the
first bright band is this one second is
this one third is this one fourth is
this one similarly first second third
fourth and so on right now let us talk
about the dark bands so where is the
militant what we did for diamonds in
case of dark bands we will consider the
condition for destructive interference
so what is the condition for destructive
interference that path difference should
be equal to n plus 1 by 2 lambda so here
path differences XD divided by capital G
this is equal to n plus 1 by 2 into
lambda so from this we can say X is
equal to n plus 1 by 2 lambda capital T
by small D so here also let us mention
it as X n so this represents forces
shape of NF dark back right so this
denotes the position of the NH drag bank
as I mentioned earlier that in this case
this end
now that we have some idea about the
fringe pattern that is the bright
fringes and dark fringes position we can
look at the graphical representation of
the fringe pattern so this is how it
looks I mean this is the fringe so if
you plot this fringe graphically this is
the intensity at the same time and that
is this represents the central bright
bank central bright Bank so this has the
maximum intensity and then you have the
two dark bands these are the two dark
bands again you have two bright bands so
these two great bands correspond to
lambda 1 lambda these two bright bands
correspond to 2 lambda 3 lambda and so
on right so this is my central bright
Bank
and these are my dark bands these two
are dark bands corresponding to N is
equal to 0 because when you put n is
equal to 0 in the condition of
destructive interference what do you get
the position will come out to be when n
is put as 0 for the condition of
destructive interference what will you
get n will be equal to 0 so this is
equal to 1 by 2 lambda D by cap LD so
this corresponds to diagram this is the
central bright band for M is equal to 0
for the condition of constructive
interference right because in this case
when n is equal to 0 it for response to
path difference is equal to 0 and what
is the phase difference phase difference
also corresponds to 0 in this case what
would be the path difference in this
case the path difference corresponds to
lambda by 2 right and the phase
difference corresponds to plus minus 5
so this is lambda by 2 and plus minus 5
how am i calculating this by using the
condition for destructive and
constructive overlap I mentioned before
also right the condition for
constructive overlap is five
differential P n lambda and the
condition for destructive overlap is n
plus 1 by 2 lambda right so using that I
can calculate the path difference for
each of these points if I know path
difference I can calculate the phase
difference because a path difference of
lambda gives rise to a phase difference
of two pipe using this I can calculate
the corresponding phase difference all
right so this is how you can understand
this fringe pattern next we will talk
about fringe width what is fringe width
it is the distance between consecutive
dark and bright fringes that means the
distance between two bright fringe this
is my fringe width so it is generally
denoted by
Veta we will denote this fringe width as
bida or we can also say that the
distance between the two dark bands that
is also Veta so we will find out an
expression for the fringe width as well
now in case of an interference pattern
it is seen that the fringe width remains
constant throughout that means the dark
and the bright banks are equidistant
from each other there is another
terminology that is called angular
fringe width what is angular range with
angular fringe width is the angle which
is subtended by a bright or a dark
fringe at the center of the two slits
right that is known as the angular
fringe width so let us first talk about
the fringe width let us find out an
expression for fringe width expression
for Vita Vita is fringe width and we
denote angular fringe width with feet
down so what is Theta let us suppose if
let us suppose this is s1 and this
h2 this is the midpoint sorry the line
is not straight because at the center
the bright fringe should come right so
the angle subtended at the center is
known as the angular fringe with the
angle which this fringe that is Vida
substance at the center is known as
angle at fringe width so let us find out
the lean expression for linear fringe
width first so what is linear fringe
width linear fringe width beta is
nothing but the distance between two
consecutive bright and dark fringes now
what would be the position of n it band
it will be n lambda capital T by D so
this is for NH bright band so what would
be the position for n plus one at bright
band it will be n plus one lambda D by D
so what is Beta Beta is the distance
between both of them that means X n plus
1 minus X M let us suppose if this is
the position of the first bank this is
the position of the first man later say
this is X n then this is X n plus 1 so
what is fringe width this is fringe this
is Vita right so beta will be xn plus 1
minus X n that is equal to n plus 1
lambda capital D by small D minus n
lambda capital D by small D therefore
you get Rita is equal to lambda capital
D by small D so the fringe width depends
upon the wavelength of light used the
distance of the screen from the slits
and the distance between the two slits
so these are the two factors on which
these are the three factors on which the
fringe width depends right so if you
increase or decrease this distance
the fringe width or will also keep
increasing or decreasing however the
fringe width throughout the screen will
remain the same
now let us talk about the angular
venture and I talked about angular
fringe width
it means this linear fringe width
whatever angle it subtends at the center
so since here I have conceded this Veta
so let me call this angle as V that
forget about the previous length so this
angle is Theta and so this is known as
angular into it so how do you how do we
find out an expression for angular
fringe width that is same let us say
this is the midpoint right what is my
fringe width range with this from this
point to this point so this distances be
done so the angle which this beta
substance at the center that angle is
known as fringe width and this distance
is D so we can see that theta is nothing
but beta by D because this theta angular
fringe width is normally very small so
we can say for small an angle theta it
is tan theta is almost equal to theta so
we can say theta is equal to beta by D
so theta is equal to lambda R capital D
by small D capital D or angular fringe
width is equal to lambda by small D so
angular fringe width is nothing but the
angle subtended by the related fringe
width at the center like at the center
where center refers to the center
between the two slits so these were some
of the terminologies related to the
Young's double slit experiment so young
promising by performing this experiment
means that light is of wave nature
because if light would have not been a
wave it would have not shown this
phenomenon of
perhaps he also explained interference
very clearly because the bans were
clearly visible on the screen using the
concepts of the superposition of waves
he was able to find out the position of
the dark and bright banks on the screen
he also found out that the fringe width
is constant throughout and fringe with
the valleys as the distance of between
the sleeps changes or the distance of
the screen from the slips changes so
these were some of the observations of
young by performing the double slit
experiment and this proved completely
that light is of believed nature so here
we end our discussion on interference
because I hope interference is cleared
up okay so now it is time that we solve
some problems based on interference so
interference was one important property
related to the wave nature of life next
we will go ahead with diffraction
followed by polarization so a quick
discussion
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