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Hello again, we are going to continue our foray into geometric optics
we've briefly touched on it when we get to the end our Snell's law derivation and we realize much easier to use
rays instead of waves, so we are going to continue our discussion today by talking about
Light wave vs. light ray; and then talk about how these rays form different images
and using lenses to make these images
and derivating the paraxial rays approximation and the thin lens equation
ended up with learning how to draw ray diagrams for lenses
so this is where we left off last time with a Huygen's principle
for transmission into a different medium, we typically draw these
wave fronts as it comes across
but as it turns out, it's much easier instead of drawing all these wavefronts
rather to draw a ray of light that is perpendicular to all the wavefronts, and it is much easier to deal with the rays themselves
which follows a very simple law known as Snell's law which we have done and dealt with
this also works for all other kinds of light waves and in cases where interference doesn't matter the
light ray is a much easier representation to think about and therein lies
the whole field of geometric optics where we don't think about the light as a wave
but more as a ray, more like a laser beam
that goes in a straight line and refracts and reflects according to Snell's law
this also works for spherical sources, so if you have a candle on a cake here, it's more or less a spherical source
and it emits spherical wavefronts like that. Good thing to point out here
most diffused reflectors, so not like a mirror, or the surface of a piece of metal, it does not look shiny, if it's a white piece of paper
what you're seeing is a whole bunch of random atoms on it that scatters light in a spherical manner
so that's why you see a piece of paper as white no matter which way you turn it
so these spherical wavefronts are useful and instead of drawing these spherical wavefronts all the time
we can just draw all these rays emanating from the light source
of course perpendicular to each wavefront as you go across
now some of these rays gets intercepted by an eye
so just look at the two outside beam
and that gets interpreted as
an object that's back here because our eye sees these two beams of light are diverging as such
following them back, it finds out where the image actually is
however the eye is not that smart, all it can see is the part that is right in front of it and that
it uses that to extrapolate and to trace back to where the object tends to be, but
we can manipulate these light rays so that the object is not necessary where this is. Say we have a mirror, very simply
the light that comes out from the light source is bent by the mirror, it is reflected off the mirror to our eyes
but our eye still traces back, because all it sees is the stuff back here
it stills sees an image back here, it still thinks an object is there, but it is not, so we give these things different names
we call the physical thing you can touch, that's the object, it emits light rays which gets transformed or manipulated
with various optical components which we will talk about and it enters our eyes, then our eyes
traces back whatever rays that hits it
back to where they crossed and forms an image
and that's what where it thinks the object is, that's called an image
if you put your hand there, you will realize that there is no cake
and another way to manipulate light ray is through refraction. Here I have a transparent piece of glass
inside, I have embedded a cake in there. I can use water instead, but that would make for a pretty soggy cake
It also changes the direction of the light beams, so that it also makes an image that is in the different spot of the object
and more often than not, same with water and glass, the image seems to be closer than the object actually is
so reaching for things in the bottom of the pool you may miss it
so there is a bit of a trick if you want to spear a fish
you can think about where you want to hit instead
so that's for a flat refracting surface, but what if we start curving these surfaces,
well we get what we call a lens. A lens, by definition, is a transparent material that's got one or more curved surface
by which you can change of direction of these light rays, with certain approximations, we can see that
certain shapes of the curve will let you put an image that is closer than the object
and if you have the curvature the other way, it will form an image that is further away from the object
what's more interesting is sometimes if you bend the light rays enough they crossed over each other
resulting in an image that upside down from the object and so
you would basically see an image in front of the lens in this case that is upside down
and if you try and reach for it, there won't be anything there, you would think it is there, but it is not
so that's why these points that we call images where the light converges again
is so interesting to us, because our eyes, all they do is they trace back these light rays
and find out where this point is, and say that the thing I see must be there
of course not realizing all the optics and where the actual object is, so it is especially important for us to think about
what kind of curved surfaces
and the spacing and the direction in order to form these points where the light converges into images