Refraction and Refractive Index - Light - Reflection and Refraction, Class 10 Science Video Lecture

so in the morning when you see sunrise
or in the evening when you see sunset
do you see sunrise and sunset the moment
they happen or do you see them later or
before in other words this light travel
really really fast almost infinitely
fast if you look at the sky you see
stars are you sure this is there because
when you look at them there's light
instantaneously reach you from them what
does it take a long time because when
the distance becomes larger and larger
you might be able to notice that light
takes some time because in real life
when you see around us what we usually
see is light is so quick and the
distances are so small that the speed of
light is hardly a measure that we have
to make
it's almost infinite so what are we
asking here does light really have a
speed that is measurable
in other words finite well the truth is
in vacuum light travels at a very very
very high speed of 3 into 10 to the
power of 8 meter per second which makes
it so that it's almost instantaneous but
even with Sun light takes about eight
minutes to reaches so in other words if
somebody turned off the Sun you wouldn't
know for about 8 minutes only then we
know which means that if you take light
and if you allow it to travel a
particular distance it has a finite
speed but does light travel at the same
speed in all media and what do I mean by
media that can travel through glass that
can travel through water there are some
media through which light can travel
you've seen that I put it through to
table just gets absorbed doesn't travel
through it but if it can travel through
it does it always travel at the same
speed it's an interesting question you
might already know that light varies its
speed depending on what medium it is in
but that's only a partly you know it's a
partly true statement because we could
confuse you all the time they tell you
that travel the different speeds in
different media why what is like form of
energy it's traveling at somebody plus
speed why does it slow down in the
medium or does it even slow down in the
medium well the truth is to understand
this you have to go into the atomic
picture or something right let's say
light is starting through vacuum what
does it have to stop at nothing so this
energy or light which is action
electromagnetic wave what does it really
do it's going around in vacuum happily
nothing to stop it but the moment it
encounters a medium what really begins
to happen there are atoms in the medium
which might get in the way of light and
which is what happens so light gets in
what usually happens is that light gets
absorbed by one of the atoms and then
gets re emitted again gets a job
it's limited again so it's not really
that light is slowing down but light is
getting absorbed and re-emitted absorbed
and re-emitted therefore there is some
time for the absorption some time for
the Rhea mission so what does it look
like towards from outside you know we
are looking at from so far away that it
looks to us as if light is just slowing
down for all practical purposes you can
imagine light to be slowing down but
it's nice to know what's really
happening inside so the true analogy is
that light doesn't slow down but light
has a lot of stops it's like not really
like if light was a bus I know the bus
is going as long as there are no bus
stops it's quite fast it enters the
medium does the bus slow down not surely
whenever the bus is moving it's moving
with a particular velocity but there are
many stops each atom is a stop for the
bus and in this case for light so when
it looks as if it's moving inside the
medium it looks as if it's slowed down
so with this in mind the biggest
takeaway for us is that light has
different speeds in different media and
how is it determined in each media
depending upon how quickly they absorb
and how quickly they DM it now based on
this we have a definition we say that a
medium in which light travels very fast
is less optically dense and a medium in
which light travels very slow is more
optically dense now I want you to know
that this density optical density has
got nothing to do with the usual mass
density which is what which is heavier
you take like one volume of say one
litre of something which is heavier
that's a different density that's mass
density depending upon how slow light is
in that particular medium we have
another term called optical density a
good example for you would be if you
take oil at oil floats on water what
does that mean it means oil is less
dense than water but if you find out the
speeds of light in oil and in water it's
a lot slower than oil
what does that mean oil is more
optically dense than water so here we've
just shown you an example of where oil
is more mass dense but less optically
dense one example to show you that these
two need not go together all the time so
with this in mind let's see what happens
when light now changes from one medium
to another because what's going to
happen when it goes from one medium to
another its speed is going to change so
let's see what happens so when we told
you that light always travels in
straight lines you already know that
light bounces off some surfaces
in one sense it's bending right in other
sense also advanced we kind of light you
and we told you light always travels in
a straight line it does travel in a
straight line until unless something
stops it when something stops it rather
gets absorbed or bouncing off which is
called reflection or goes through but
when it does go through does it continue
to go in a straight line
or does it do something that's called
bending so will light Bend when it goes
from one medium to another that's a
question now we know one thing
everything in this chapter comes out of
one fundamental principle and what is
that light is in a hurry
light wants to go from one point to
another as quickly as possible so it
takes the quickest path now how do we
know this or why is this true we don't
know what we call this for mass
principle of least time so let's see if
we can just extend the same analogy and
understand whether light will Bend if it
will Bend how it will Bend which
direction will it Bend in all those
things so to do this let's take a very
very interesting analogy let us say
three friends right three of you guys in
this case are walking along the shore of
a river out of the sea or whatever it is
and all of a sudden you watch a gorgeous
woman sinking that she's screaming for
help somewhere in the middle of the
water and all three of you know how to
swim and you decide this is your chance
and to get her attention and become the
hero because all of us watch these
movies so what you decide to do so three
of you or one of you is like extremely
enthusiastic you're the kind of guy who
thinks like you know oh my I have to do
this so you start running right at her
so what kind of paths will you take you
start running right towards her so you
reach the water at some point then start
swimming but if you're a little smarter
what would you do because you know that
most people can run a lot faster than
they can swim right so you'd probably
run a little bit more and then arrive at
an angle and then start swimming towards
it so the who's gonna win really is the
guy who's good really enthusiastic who
runs right hatter reaches the water
start swimming yes him a lot more afraid
as you can see so he starts off he goes
straight at her and then he starts
swimming that much right do you think is
going to reach first or do you think
this guy who's going to do that is going
to reach first right so one of those
parts is going to be more than or more
efficient than the other path which
means that the quickest path need not
always be the shortest path and you
already know this if you were to go if
you stay
in India or any other part of the world
you know that
a straight line part that connects two
points in the city might be throw main
road and you'll never ever reach one
time but you can take like a little
shortcut of course it's a lot longer but
you reach faster because there is no
traffic there is similar analogy here so
what do you observe the shortest path
need not be the quickest path but what
part that lies that doesn't light always
take it takes the quickest path so let
us now begin to notice what is the
quickest path it's not a simple problem
right you might also ask how does light
know it has to take the quickest path
you don't know how does light find the
quickest path and also we don't know or
rather if you really want to know about
this we'll have to go and understand
what light really does when it behaves
is a wave right but in one sense here we
really don't know how light fell figures
out but it does figure out doesn't it so
light always picks up the quickest path
and as you can notice if this is land
and this is water the light starts red
it's not going to go straight that way
it is going to go here and then take
that path because it wants to spend as
much time as possible on land where it
is faster and as little time as possible
in water where it is slow so people are
asked you why does light Bend then a
trivial answer would be because the
speeds are different but a much better
answer is to say speeds are different
and light wants to take them with his
father therefore it bends that way of
course light will do something stupid us
go and come back like this I'd be really
stupid because the worst case path is
and down there straight right now the
question really is wave will the bending
be more when will light Bend a lot more
what appears to us as bending is when
light wants to spend more and more time
in the faster medium which means that if
the speed the ratio of these speeds or
the difference in speeds is a lot then
the bending will be more that makes a
lot of sense doesn't it so what is this
bending proportion it's proportional the
difference in the speeds or the ratio of
the speeds of these two media the slower
install the second media's the more and
more light wants to spend in the first
medium another with this in mind you
keep this in mind we'll give you another
analogy for you to be able to understand
how light rail events for you to think
of this think of yourself riding on the
highway you're riding a car on the
highway so you're going really fast and
you see somebody saying in clay so you
order your gonna turn and go into the
clip let's say right so you're
approaching let's say you're a car and
you're approaching
from Road so the moment you hit your
interface which we will catch the clay
first so what's the assumption here you
can travel faster on the road down on
the clip by resumption so you'll write
wheel touches the clay first I know what
do you observe after that that will get
slowed down but who hasn't got slowed
down yet the left wheel so what happens
when one wheel slows down and the other
wheel does not slow down two wheels are
going at different speeds what happens
when that happened turning right so the
car is going to turn that way and then
start continuing straight because once
both the wheels will touch the clay both
are going at the same reduced fee that
turning happens only when one Reed is
going slower or faster than the other
way right so if you imagine it this way
it becomes really obvious doesn't it
right a car coming here it's it and
starts continuing at another angle now
what's really interesting is that look
at the car as it comes straight down at
the road from the road to the clay does
it turn it won't turn because both the
wheels will hit the hit the clay at the
same time similarly if you imagine a
lighter even with our old analogy if the
light ray is approaching perpendicular
due to the girl right if you're on the
shore and if you see the girl running
and if she is right at you right in
other words is perpendicular to the
shore then all you have to do is run
straight at her doesn't matter there is
no angle to be worried about so the more
and more oblique you are the more and
more you will be bending so we have done
a little bit of intuitions about why
light bends how much it bends and where
does it all come from the only principle
we know for the entire chapter for mass
principle of least time all lights in a
hurry so from that you can pretty much
drag everything else so let's there have
a little law for refraction which is
what it's called because you haven't
really spoken about that word till now
we have kept saying bending bending
bending but what do we mean by this
bending when light travels from one
medium to another when it bends it's
called diffraction yeah it's not because
of refraction light doesn't Bend because
of refraction it bends and it's called
refraction
let's see a little bit about it in our
next module so we kind of qualitatively
saw what light does when it enters from
one medium to another because there is a
speed change light bends
why because it wants to take the
quickest path now let us make this more
mathematical and formal so that we can
start making calculations based on it so
let us start naming certain things and
let's take a light ray
the light rate begins and goes through
air for example and enters gloss right
so it's going to go like this and it's
going to bend that way
great now let us draw a normal right and
let us measure this angle as the angle
of incidence and that angle is the angle
of refraction and not reflection so the
fraction so if I and EF are now how are
these two related
we know that the greater and greater the
difference between these feeds the more
and more the bending will be so let us
try to understand let's take the ratio
of the signs of these angles and we'll
see why we do that you kind of can see
that you know the sine is the opposite
by the hypotenuse so we're kind of
trying to take a measure of how much
bending is really is right so the more
and more the sine is the larger larger
the angle is so in one sense measuring
sign is like measuring the angle itself
because the sine is proportional to the
angle so we'll take the sine of the
angle if we take Sinai by sine R you
find that it is a constant for a given
two pair of media and it's called the
refractive index of that two pairs of a
media of or that two pair of a media so
your media one and you have media to
then Sinai by sine R is called the
refractive index of 2 with respect to
one because the light entered from one
into 2 therefore you represent that
right Sinai by sine R as say R to one R
of 2 with respect to one I'm using a
prettier ad-hoc convention here there's
not really a very very standard
convention but we can do this now what
turns out to be even more beautiful is
that that lifter active index which is a
random number right yeah for thousands
of years with all that reflective Indic
is a random number which is a property
of two media but after formost principle
of least time you understood something
very very very interesting about and
that is that refractive index actually
corresponds to a very very very physical
representation of the speeds of light in
those particular media so if you were to
write this sign I by sine R equals the
refractive index of 2 with respect to 1
that is also equal to the velocity of 1
by the velocity of 2 velocity of what
velocity of light in 1 by velocity of
light into clear clearly there is a
difference within velocities otherwise
light wouldn't Bend so if you notice
right now what is this refractive index
it is nothing but the ratio of the
speeds in
to media it and the greater this ratio
the more the refractive index and
therefore more the bending makes a lot
of sense doesn't it so we don't really
have to remember this is a random thing
but what is this really a measure of how
much the slight bend and what does it
depend on the ratio of their velocities
so to bridge these two they have a
quantity called the refractive index
which is nothing but the ratio of their
velocities now with this in mind that
particular quantity that we derived or
that particular equation we wrote sinai
by sine R equals refractive index it is
also equal to the speed of light in the
first medium by the speed of light in
the second medium is called Snell's law
there is a pretty interesting derivation
for this which we can do we won't go
into it right now right you might want
to learn about it if you want to learn
about it go ahead and do it but the way
to derive this is by understanding a
very fundamental principle about what
light really does what is light trying
to do take the quickest path right you
go a little deeper but you will
understand this if you calculate the
quickest path and calculate sine I by
sine R you'll get the ratio of those
velocities you can go ahead and do that
so to derive right now is Snell's law
now let's take the opposite case because
we know the law of reciprocity and what
does it say whatever light does in one
direction if I invert the whole thing it
will do exactly in the other direction
so if light started off from glass and
enter air what would it do it would come
this way and then start going the other
way in other words will Bend away from
the normal what did it do in the first
case it bent towards the normally so if
you take this into account and you start
observing what happens the biggest
takeaway from this little part is that
when light enters from a rarer medium to
a dense the medium it starts and it
enters a denser medium it vents towards
the normal and vice-versa if it starts
from a rare denser medium and goes into
a rarer medium it bends away from the
normal
now that is one of the biggest takeaways
because most of what we do in refraction
can be boiled down to this fundamental
idea does it bend towards normal or does
it Bend away from the normal now the
really keen ones amongst you might have
noticed something it let's take a case
where the light enters from a denser
medium to a rarer medium and look what
happens I make this I start a ray of
light it goes out - it bends away from
the normal I make it even more wide it
bends even more away from the normal I
keep doing this what's going to happen
eventually
that's right light is going to hit and
start going parallel to the medium and
at that point we say light
is that a critical angle because what
light goes to the other medium nothing
right all the light is going parallel
between right at the interface itself so
then what would happen if I increase the
angle even more like you see it's going
to get completely reflected back into
the old medium itself was there a mirror
no just by refraction or where light
bends light bends so much that is going
to start entering its own medium so
there is a critical angle at which you
can send light because at that angle any
greater angle than that light will not
go to the other medium it will just get
reflected back interesting so this
principle is called total internal
reflection because all the light is
totally reflected inside and it's pretty
useful in a lot of places whether you
see a mirage or whether you see you know
little little blots of like a little
blots of water on road right you've seen
a very hot road on a long day if you're
driving on the highway you'll see little
patches of water you can explain that
using this how do optical fiber cable
works a cables work cable works I said
you know how the optical fiber cables
work they carry communication throughout
the world they carry light such that it
gets totally internal reflected these
are all little parts that you might be
really interested in but the fundamental
crux of this idea is that when light
enters from one medium to another it
bends following a very very reliable
pattern of sinai by sine R equals the
refractive index or the speed of light
now let's take this one step further
what if for every pair of media in the
world you have to find out the
refractive index with respect to each
other how many pairs of mean let's say
there are 10 media in the world of
course there are a lot more how many
should you do a lot right if you're in
if you're into permutations and it's 10
C 2 and how much is that
and in the 9 by 2 or 45 so 45 different
experiments have to do ok how much the
Sinai by sign out here
how much is sign a by sign out there but
you don't really have to do that because
of formas lease Princip principle of
least time what does it tell us the
refractive index is not a random number
it is a ratio of the velocities which
means all you have to know is the
refractive index of one material with
respect to say a standard material say
vacuum so you find out the refractive
index of each material or each media
with respect to RQ
then you can keep calculating for all
the other possible pairs so now if you
have 10 media out of which one is vacuum
how many how many times should you make
an experiment only 9 times so now you
know all the rack
with respect to vacuum and then you can
calculate for each other let's take an
example let us say you have glass and
let the refractive index of glass with
respect to vacuum be called refractive
index of glass and let the refractive
index of water with respect to vacuum be
called refractive index of water now how
would you find out the refractive index
of glass with respect to water in other
words when light enters from water into
glass or from glass into water what's
going to happen in order to do this what
do you have to do all you have to do is
just divide these two quantities because
we know that refractive in water is
going to be velocity of light in
velocity of light in vacuum by velocity
of item what so if we divide these two
what do you get exactly the quantity
that you want velocity of light in water
velocity of light in glass pretty simple
right so this kind of foremost principle
release time makes it so that all you
have to have is a refractive index with
respect to some standard medium and then
you can calculate for any pair of media
just by dividing the corresponding
refractive indices so with all of this
we've covered a good amount of ground
here you've done Snell's law and you
understood how the fractal indices
really work by division so now that
we've understood what refraction is and
we also understood what Snell's law is
let's take our first object to play with
let's take a glass slab so what's a
glass slab it's something that's like a
rectangle or a cuboidal piece of glass
and let's see how light really begins to
behave when it passes through this glass
slab so beginning to play with our first
object here let's see what happens so
let us take a little glass slab let's
place it out here so that it's here and
then let's light let light start coming
towards that we know that light is
entering from rarer to denser because
air is rarer than plus so it's going to
bend a threat towards normal great good
up till here but the glass slab ends
after a point of time so the light has
to go from glass into it and that is
denser to rarer so what's going to
happen it's going to bend that's right
away from the normal wonderful so we
have a pretty simple Pixlr light enters
bends towards the normal then goes away
from the normal right so but what does
it look like you does it look like the
lights Direction has been altered light
came in a particular direction at some
angle has it changed finally or is it
going the same the same direction that
it came from of course you can see that
it's a little split right from wherever
it would have gone now it's been a
little
deviated yeah but is it still going
barley to the original direction or has
a direction change itself you don't know
it might look parallel but that doesn't
mean that it is parallel so let's try
and understand whether it is really
parlor or not so to do that it's
something very simple let's mark out
some angles here and what we will begin
to do is that we know that the first
angle is called a tie one second angle
let's call it r1 so sign I 1 by sine r-1
we know what it is
that's the refractive index of glass
with respect to air all V air by V Blas
great now let's name the other two
angles I 2 and r2 and that is what sign
I 2 by sign r2 equals what the
refractive index of air with respect to
class or velocity of glass by velocity
of air and I'm saying velocity of glass
I think you know what I mean velocity of
light in glass the velocity of light in
air see those two equations grid now
what do you observe your top velocity of
air by velocity of glass and bottom
velocity of glass velocity then there is
a broken rate so you can forget them and
just equate these two US reciprocals and
now that you've done that let's observe
one more thing you've all learnt our
geometry really well so we know that if
there are two parallel lines there's a
transversal that cuts it then those two
angles call the alternate angles are
equal and do you observe a pattern here
or is there an alternate angle here
alternate angles you're yes there is so
r1 and i2 are alternate angles great so
what you have to do now they're equal so
you might as well replace them one with
the other so if you do that what do you
get
that's right you get sine I 1 equals
sine R 2 in other words I 1 equals R 2
what we just proved here yeah that
particular angle we began with is equal
to this particular angle with which it
leaves so very clearly very easily if I
extend that line out here and if I draw
something like the normal X in the
normal up there you can very clearly see
right if you take this and draw out
there you can very clearly see that what
we've just proved what have we proved I
1 equals R 2 also clearly proves that
the two lines are parallel which means
that a glass slab doesn't really Bend
light
all it does is displaces light a little
bit right while the light is in the
glass it moves in a different direction
but once the moment is out it's back to
its original direction
so with this in mind we've kind of
understood what a glass lab does why is
this useful you will see and you've also
proved we've used as an excuse to use
our Snell's law get more hands-on
experience with it and prove that the
light that comes out of a glass lab is
parallel to its original direction but
does a little bit of deviation now it's
time to play with something very very
interesting from what you've just learnt
because it's always more fun to stretch
ourselves beyond what we usually know so
let's ask a simple question I take a ray
of light senator Padilla angle it so and
then from air let's say it goes into
water or glass let's say from air it
goes into glass right so simple case
light going from air into glass we all
know what happens what happens it bends
towards the normal clean so you see it
out here wonderful now let's take
another case just that over here instead
of air going the other light going
directly from air into glass what we are
going to do to it is that we put a layer
of water in between so air goes through
water then into glass now the question
here is both cases light emerges in
glass so it's going to be traveling
through glass would it throughout at the
same angle or the water in the middle
would it make a difference that's the
question right so does the water in the
middle really make some kind of
difference to the final emergent angle
of light so should it or should it not
now we can probably do this using math
yeah sinai by sine R equals the
refractive index over here sine of SNR
equals refractive index between water
and air sign and set by sine alpha glass
and water then you can calculate you
might get the answer to be that it does
not make a difference but let's just try
and understand how we can do this in a
more maybe slightly more beautiful
manner there is kind of imagine that
between glass and water here so you have
air your water and you have lost in the
second case right so three media let's
just imagine for a moment that between
the water and glass there is a very very
very very thin gap it an infinitesimal
gapless you call it a very very small
gap and what do we know about glass
slabs
right in this case what forms the glass
slab or water because it's any
rectangular piece is as good as a glass
slab so air is going to light is going
to enter from air into water it's going
to bend towards the normal and just as
it leaves water what is it going to do
it's going to emerge outside and just
enough previous module on glass slab we
prove that these two rays
to be parallel what does that mean it
means that as far as the lights going to
exit water in a parallel manner we can
forget the water exists so what does it
become equal to now the second case
becomes exactly equal to the first case
right because as long as the air would
light that enters water exits the same
way as it came is it really matter if
the water is there so remove water what
do you get no light entering glass so we
are confirming that the two rays are
going to go in a parallel manner so the
number of media in other words to
generalize I can start with media a and
I can add n media in between BCDE F as
long as light doesn't get total
internally reflected back when it
emerges out if it does emerge out of the
last medium it will emerge out in the
same direction as if all of them had
been removed and just the two media are
put together right so that's one
interesting kind of corollary to
understanding Snell's law in a very deep
and fundamental man