Refraction through glass prism 001 Video Lecture - Class 11

today we are going to study the
refraction through the glass prism what
is a prison it is the first question
which had come in your mind after
listening the top a prism is basically
an attractive medium bounded by at least
two non-parallel reflecting surface but
the simple most simple prison we have
taken and we have normally observed in
the labs is that in which there are
three rectangular three rectangular hear
the cars are showing three rectangular
non parallel surfaces and two triangular
faces these triangular faces are
parallel to each other and with the
three particular surfaces are not
parallel to each other this angle is
called the angle of prison and it
depends that the angle is very less or
baked or the prism is equilateral and
accordingly the properties of Christmas
changes if this edge you can see this
edge is called refractive edge of the
prison and these surfaces to which the
light rail reflect a contacting surface
now if the prism is on this side it is
upright then it is called the base now
we want to study that how the lighter
behaves when it falls through a prism
I go to it so let's have another diagram
in which we can show that how the light
rain falls and behaves when it go to a
prison hear this Ray a B which is the
rail which falls on the surface small be
a this is the reflecting surface of the
prism and when the incident light a B
falls on it it undergoes the process of
refraction this blue line is showing the
normal which is perpendicular on the
surface of the prison and the light ray
which is incident and the light ray
which is refracting that is bc is
actually reflecting at an angle which we
have named our one now if we go to
further then bc light ray propagates and
reach up to the second reflecting
surface which is a small a see now at
this reflecting surface the light rain
again it suffers through the refraction
and here when the light ray is coming
outside the prison it again burns and go
to the emergent angle which is denoted
by small now these refractions
mathematically and here first of all as
we have gone as we have go through the
process what so the ray a B when it
falls on the surface a B then it
actually is moving from here
to the glass video and as we know that
the glass is optically denser than the
air so the light ray a be back towards
the normal and the angle of refraction
for the surface a B it is our one but
when the BC light rail propagates and
reach Judy surface AC then it bands away
from the normal as it is moving from
blast through air and when the light ray
travels from denser medium to related
media it bands away from the novel and
the incidence angle is lesser than the
refracted angle in this case so now we
want to calculate that what is the
relationship between the angle of
deviation and the angle of incidence and
angle of emergence and the refracted
islands so to find the angle of
deviations numerical expression first of
all we should know that what is the
angle of daeviation angle of deviation
is calculated between the original
direction of the incidence rate and the
refracted ray so we can define angle of
deviation as the angle between the
original direction of incident ray which
is in the diagram at surface a B it is
denoted by it is shown by the rey de the
line ve now a B is the incident ray and
de is the shrink the original direction
of incident ray but when we talk about
the reflected
the refracted ray is b/c so here the
angle of deviation is Delta 1 which is
angle em be see now this is the angle of
deviation as it is telling us that how
much the light ray has been deviated
from its path while it is moving through
the search interface of the air and the
glass medium so here in the diagram you
can say that in an octave a shin which
is denoted by angle BM angle mbc is
equal to angle in b a- angle c.b.o now
how we have returned this mathematical
expression you can see from the diagram
that this angle which is denoted by I it
is the angle of incidence and here this
angle is actually shading the vertically
opposite angles that is if you want to
see then this angle is having a word
tickly oppose affair with this now if we
are saying that this Delta 1 and Arwen
are combining showing that vertical
opposite pair of I then Delta 1 can be
written as engl i minus in ganado so we
are getting the value of Delta 1 Delta 1
is equal to angle NVA in the diagram is
showing in the eye and minus inner CBO
is denoting the refracting anger
and it is 44 surface it is denoted by i
1 so this is our equation 1 now let's
come to know let's discuss that how
Delta 2 can be expressed in terms of e
and r do this arto is the angle of
incidence if we are taking the light
rain moving from glass prism to the air
outside now this r1 is the incident rate
and e is the emergent angle now if you
can see again then similarly as the last
process angle e is equivalent to it
Delta 2 plus r2 which is T on the law
which are the two angle of vertically
opposite pairs now here also we can
write that angle em c d is equal to MC
be in the diagram here the curse is
showing that ingles em c and me it is
the angle of deviation which is the
angle between the refracted ray and the
incident rays direction so this is the
angle which is showing that how much the
refracted rate has been debated from its
original path swinger MCB is equal to
angle in-dash CD minus angle 0 c b then
when we are going to write it in the
terms of the same symbols we have used
then angle MCB is denoted by delta 2 and
it is equal to e minus angle 0 CB is
doing fine art so we have observed this
is our equation number two now
if we show that if I see that in the
whole process of these two refractions
if we totally find out the angle of
deviation then it will be the angle
between the incident ravages which was
the original incident ray and it is B is
the original incident direction and the
finally reflected ray and the finally
refracted ray that is C D when it is a
extrapolated back then it coincides with
the original direction of the incident
ray at em so the angle between the
original direction of incidence rate and
the refracted Ray's direction it is
giving us the angle of daeviation that's
why I here it is the total deviation
which is in between the original
incident today correction and the
finally emergent race dash so I to get
the value oh I of r1 and r2 in terms of
to get the value of r1 and r2 in terms
of anger of prison let's see the
quadrature which is shown in the above
diagram closely it is the Engel of
prison a this is the edge it is the
vertex a small a and the B point is the
point of incidence and 0 is actually
that point at which the normal needs c
is again the point which is the point of
incidence for a second surface and here
Delta 1 and the other two are the two
angles which are the deviations and
Armand in auto auto angles which are
inside the prism
one is the retractor then and swindles
incident angle for a second surface
Delta is the angle of daeviation now we
are going to calculate the value of
alpha in our true in terms of a in a
quadrilateral small a capital V 0 C we
can write that angle a plus angle a B 0
plus angle Oh see a plus plus angle B 0
C are the four angles of the coordinator
and falling and sound for a quarter
nature it is equal to 360 degree right
so we can write it as that they oppose
it angles here at this point as the Blue
Nile the blue dotted line is showing the
normal that's why if we extend this line
then you can clearly see that as the
normal is opening in all the surface
thus if this angle is 90 degree then
similarly designed it should be 90
degree showing at a be 0 and angle HC oh
that is we are saying that engl small a
V 0 is equal to angle a see
engl a ce o-- is you question 90 degree
because these are formed by the Norman
and represent surface and normals n 0
and n 0 dash I perpendicular to the
surfaces so this is the clear simple
logic of taking dangle apo and a cos
ninety degree so students let's recall
let's recall that what we have done in
the last few minutes if we have to find
out the value of r1 and r2 in terms of
some known angles so we are doing the
exercise mathematical exercise in the
quadrilateral apoc and as the for angle
sum for the quadrilateral is equal to
360 degree should we have written this
equation now engl ABO an angle a co
comes equal to 90 degree because they
are found by the normals and the surface
of the prism all right now if we are
saying that in the AVO an anger issue is
it was romantically then we should use
this information say it is the equation
so first of all this equation is forward
and it is we are numbering it five then
using the information from five we put
this these values in equation for and
we'll get the inner a that is an angle
of prison plus 90 degree plus 90 degree
is your costume in the VLC
in an A plus 90 degree plus 90 degree
and VLC and all sum is equal to 360
degree and you can again write that
angle of prison plus anger do you see
should we question well it didn't this
is our equation number six so one
equation we have got in terms of in an
eighth inning of you see now if they all
serve let's triangle in the vc or then
in triangle we see oh by the triangle
property that the three angles of the
triangle always makes the combination
equal to 180 degree then we can write
here in the saw with this diagram we can
have engl are one less angle are to play
sangalo should be going to qualitatively
let's write it in here add 1 plus item
plus Engle V 0 c is equal to 180 degree
this is equation 7 on the equation 7 has
a logic triangle some property of
mathematics child somehow buddy say that
all the three angles the sum of all
changes should be quantitatively so when
we compare the equation 6 and 7 then the
RHS of both the equations are seen
that's right we should write in your A
plus angle D or see that is the left
hand side of equation 6 should be close
to left hand side of equation 7 which is
r1 plus r2 plus in the v OC as in a dios
is common in both the sides so they can
make it it just with each other and
that's why we are remained we
in the a is equal to r1 plus r2 where
angle is what we have observed that it
is the angle of prison which you can
measure simply by taking the prisoner so
we are in equation 8 we have got the
value for which we are doing the whole
exercises now if we go now if we go that
what is the significance of this value
then we should here we have a
relationship which we have already
derived between the angle of daeviation
delta and angle of incidence and angle
of emergence I and II and the two angles
r 1 plus r 2 which you got inside the
prison if it puts the r1 plus r2 value
which is equal into angle of prism as we
know that we have engl r1 plus r2 is
equal to in your logo prison so we can
use this value in this equation and can
get the result so since delta
is equal to i plus a minus of some of
our 1 plus pattern so if we put the
value from equation 8 it comes equal to
i plus a minus inner of Christmas this
is this combination is equivalent to the
angle of deviation and we can write it
as Delta less a is question I plus e so
it is the result for which we have done
all the mathematical exercise is here
and it is of much use in the optics
little prison let's have let's have a
new I could so we have in America in
which we are given that a real flight it
is a passing tone glass prism so we can
make a diagram here here is a glass
prism and light rain is moving through
it such that angle I is equivalent to
angle e this is the incident ray this is
the first refracted ray and it is the
second refracted ray and for the normals
let's have different color so the normal
n and here normal is this English this
angle is the angle of incidence and this
angle is anger of emergence and this
question says that angle I is equals to
be here so again if we come to the
diagram then it is given that angle of
prism is equal in two so did agree that
is given in the question also we have
given that angle is equal to three by
fourth of angle of Crescent so angular
prism is given as
30 degree value so let but let's put the
value 30 dealing now we have the two
information if I is equal to angle of
emergence and the secondary information
we have that the angle of emergence is
according to three performed isn't that
exciting now let's solve this question
as we know that Delta plus a is equal to
i plus e Delta's angle of daeviation a
is angle of prison I is equal of
incidents and he is in love emergence
from equation 1 or the given information
that I am we are equal we can write it
as Delta plus a super Stu choice of
angle of emergence but as we know from
equation 2 that angle of emergence is
equivalent to three x 40 angle of prison
that is equivalent to 30 degree if we
solve this value will come children come
to the value go into 33 by four into 30
degree it is equal
this value becomes equal to 1.5 into 30
degree so when we have to find the angle
of deviation value and we should write
it as a 45 degree minus l sent to the
arches and it is equal to minus of 30
degree so delta x equals 2 with changing
this is what we have to go