Refraction Through a Glass Prism Video Lecture | Physics for JAMB

hello friends this video on ray optics
part 37 is brought to you by exam furor
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videos to the part 36 before going ahead
with part 37 now that we have studied
about the diffraction of light by many
different types of optical materials for
example the spherical mirror there are
the spherical surfaces as well as the
lenses now it is time to study about
refraction by another optical element
called prism I am very sure that all of
you would have seen prism in your
physics labs and maybe you have worked
with prisms as well what our prisons
what our prisons basically prism is
nothing it is a transparent optical
material with flat polished surfaces
that refract light so that means since
the method prism is made now it is not
necessary that prisms are always made up
of glass they are sometimes made up of
glass sometimes even plastics or
chloride depending upon the type of
application it is used for because there
are a wide variety of applications where
prisms are used so but that most
important property of prism is that it
refracts light not only refract slight
prism also disperse light that means if
white light is passed through prism it
gets dispersed into its constituent
colors that is all the seven colors get
comes out of the prism so these are some
of the properties of a prism normally
that now prisms also come in different
kind of structures different shapes and
sizes but however the traditional prism
is the triangular prism which is shown
here on this figure it looks like a
triangle wet did some five flat surfaces
so it gives a triangular look somewhat
like this as you are seeing here so now
we will see how does refraction of light
takes place in case of a prism so before
that let us
this is a prism variable we talk of a
prism what we remember is the dispersion
of light white light going in at all the
same impulse coming out right so the
terminal art is related to a prism our
incident ray the Ray which enters the
prism refracted ray the Ray which gets
refracted inside the prism emergent ray
the Ray which comes out of the prism
that means there are three rails here
which will be involved in case of a
prism so there let us suppose if this is
my prism the Ray which is entering that
is the incident ray after refraction
this is the refracted ray and the Ray
coming out that is the emergent ray
angle of daeviation angle of daeviation
is nothing but the angle which tells us
how much the emergent ray deviated from
the original incident ray this is the
original incident ray right so how much
this emergent ray deviated from the
original incident ray that is shown by
the angle of daeviation angle of prism
what is angle of a prism this angle of
the prism is known as angle of a prism
now let us look at the refraction by a
prism let us suppose this ABC represents
a prism this ray p represents my
incidentally this ray reaches here it
enters from a rarer medium to a denser
medium because glass being a denser
medium than air so it gets refracted
that is it bends towards the normal
then it again reaches this surface where
it again moves from a denser medium to a
rarer medium so it moves away from the
noun 1 so this ray is the emergent ray
and what does the angle of daeviation
how much the emergent ray deviated from
the incident ray this was the incident
ray this was the emergent ray so this
angle Delta is the angle of daeviation
now let us look at it mathematically in
this quadrilateral
in the quadrilateral a Q n R so a Q n R
is a quadrilateral in this quadrilateral
we can see that this angle of prism E
Plus this angle Q n R this is equal to
180 degrees because in any quadrilateral
the sum of the opposite angles is equal
to 180 degree right
also in triangle Q M R we can say that
in triangle I am sorry in triangle Q n R
in triangle Q and R we can say that R 1
plus R 2 plus angle Q n R is equal to
180 degrees or we can say that angle Q n
R is equal to 180 degree minus R 1 plus
R 2 right so this is my first equation
this is my second equation so put angle
Q and R in first equation so if I put
the value of Q and R this value in first
equation what do we get angle a plus 180
degree minus R 1 plus R 2 is equal to
180 degrees so this 180 and this 180
will get cancelled so we get that angle
of the prism is equal to R 1 plus R 2
now let us consider the triangle M Q R
or triangle Q M R now let us consider
this triangle in this triangle this
angle Delta is the exterior angle the
exterior angle will be equal to the sum
of the opposite interior
let me call these angles as angle 1 & 2
so this Delta will be equal to angle 1
plus angle 2 all right so now what is
this angle 1 this angle 1 is nothing but
angle I because this angle I is equal to
this total angle because they are
vertically opposite angles so we can
write that angle 1 is nothing but angle
I minus R 1 similarly we can say that
angle 2 is nothing but this angle e that
is the angle of emergence and the e
minus R 2 so we can write I plus e minus
R 1 plus R 2 so from here we can say
Delta is equal to I plus e minus R 1
plus R 2 what is R 1 plus R 2 R 1 plus R
2 is equal to a so this we can write it
as a so we can say that the angle of
daeviation of a prism is equal to angle
of incidence plus angle of emergence
minus the angle of the prism so this is
how the angle of daeviation is related
to the angle of incidence and angle of
emergence and this is how that
infraction takes place in case of a
prism so let us look at the relationship
between the angle of daeviation and the
angle of incidence now we see that from
this graph we see that as the angle of
incidence increases the angle of
daeviation keeps decreasing so from this
relationship angle of daeviation is
equal to angle of incidence plus angle
of emergence minus angle of the prism so
you see that as the angle of incidence
increases this angle of daeviation keeps
decreasing and when it reaches a point
where angle of incidence is equal to the
angle of emergence
then the angle of daeviation is the
minimum and then again it starts
decreasing so the angle of daeviation
basically keeps decreasing with the
it is an angle of incidence it reaches a
minimum value and then again keep
increasing so minimum angle of deviation
that means angle of daeviation Delta is
minimum this angle of daeviation is
minimum when angle of incidence is equal
to the angle of emergence now we will
talk about the minimum angle of
daeviation in the next slide let us now
see under what condition the angle of
daeviation becomes minimum now it is
seen that the angle of daeviation that
is Delta is Delta minimum when the
refracted ray goes parallel to the base
of the prism that means this is the
raven this ray is parallel to the base
of the prism then we see that that the
angle of daeviation that is Delta is
minimum that is Delta is equal to Delta
minimum when I is equal to e that is
angle of incidence is equal to angle of
emergence and r1 is equal to r2 because
when this line is parallel when this
line is parallel to this line the angle
of incidence is equal to angle of
emergence and r1 is equal to r2
therefore we saw that a is equal to r1
plus r2 that is angle of prison so angle
of prism becomes a 2 R so R is equal to
a divided by 2 therefore what will be
the minimum angle of daeviation so angle
of minimum daeviation will be equal to
AI plus e minus a so i plus e what is i
plus e yi and i are same so i plus i
minus k so this is equal to 2 i minus a
so from this we can say that the angle
of incidence is equal to a plus delta m
divided by 2 so when the angle of
incidence
is equal to this value then de when the
deviation that is the angle of deviation
will be minimum so the angle of
daeviation how it varies with the angle
of incidence it decreases with the angle
of incidence reaches its minimum at a
particular point when angle of incidence
is equal to the angle of emergence
now when angle of incidence becomes
equal to this angle of emergence then
this R 1 becomes equal to R 2 and as a
result this line becomes parallel to the
base of the prism so in this condition
the angle of incidence I will become is
related to the angle of minimum
deviation as a plus Delta M by 2 thank
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