Formation of Rainbow Video Lecture - Class 10

surely you've seen a rainbow maybe you
were chasing tornadoes and happened upon
one but did you ever notice that the sky
is darker above a rainbow than below I
never did until someone pointed it out
we're going to find out why this is so
with the help of refraction of light
dispersion and the incomplete story
you're usually told about why rainbows
form this story starts with refraction
the bending of light as it moves from
one medium like air to another medium
like water at an angle light actually
slows down in water visible light would
take 11 minutes instead of the usual
eight to get from the Sun to the earth
if there were a giant ocean in between
so as light flows down when it enters
water the beam is forced to turn but
unlike the constant speed of light in a
vacuum the speed of light and water
depends on the color violet light moves
slower in water than red light so it
will Bend more as it enters the water an
incoming beam of white light will be
spread out and separated into a spectrum
of color we call this dispersion now
let's take this white light beam and
send it through a droplet of water some
of the light will refract into the
droplet then reflect off the back and
refract back out to travel down to your
eye typically at an angle of 42 degrees
between the incoming light and the
outgoing light this can occur in a
circle of droplets so if the ground
weren't in the way rainbows would be a
full circle here's the fun part
violet light refracts more in the water
droplet than red light as we discussed
so violet light should end up exiting
higher in the water droplet than red but
if we look in the sky red light is
clearly higher than violet light what's
going on well if you're observing from
down here this water droplet will only
send red light to your eyes and the
violet light will pass above you it's
the droplets down here that send violet
light to you and the violet light will
appear to be coming from lower in the
sky as it does and that's how we get our
colors in the rainbow from rain and Sun
end of story but there's one part I
never understood why should all of the
light enter the water droplet right at
this point well the answer is it doesn't
some red rays enter here some enter here
and they all exit in different
directions if we add back in the other
colors you end up with an exiting
jumbled mess of color this mess of color
should look white
but it definitely doesn't so what's
going on this is where it gets more
complicated than you usually hear as
this red light ray enters higher from
the midpoint it exits at an increasingly
large angle but watch what happens here
eventually the Ray turns around no
matter where red light enters the
droplet it can't go past this angle
that's the maximum angle and it's 42
degrees for red light it's slightly less
for orange and yellow and so on until
you reach violet where the max angle is
40 degrees so it turns out that at that
maximum angle you also get a maximum
brightness so even though all the colors
can reach here around violets max angle
because their maximum is beyond that
violet is at its maximum brightness so
it stands out against the other colors
same goes for the max of the other
colors below violet no colors are at a
maximum so all the colors mix again and
form white that's why this guy appears
lighter below the rainbow than above
none of the light can make it out above
red so the sky appears darker then how
did this second rainbow sneak up there
well you'll notice the colors are
flipped in order and again that the sky
is lighter above them that indicates
that the light had to reflect twice
inside the droplet in order to get the
right angle down to your eye it actually
had to enter the droplet from below the
midpoint and you get a double reflection
causing a second rainbow now this story
is complete
the end
[Music]
[Music]