Transcript Slide 1

October 15 – outline:
What we did last time – “memory refresher”:
“Pedroni”, Page 8, laws of light reflection.
Next, start taking about refraction of light:
“Pedroni”, pages 10-11 (basic facts).
Then, continue with this PPT presentation.
Basic facts: light incident on a water
or glass surface, is partially reflected,
and partially refracted:
Explanation why
objects in water
seem to be closer
to the water surface
than they actually
are – which causes
the “broken stick”
effect.
Refraction may produce spectacular
Visual effects:
More about refraction, and
total internal reflection
c - speed of light in vacuum;
V - speed of light in a medium.
Vacuum
Medium
c
 n is therefractive index
V
of themedium relative
to vacuum.
* If we only say “refractive index”, it by default means “relative to vacuum”.
If the ray impinges on the surface from vacuum, the angle of incidence,
the angle of refraction, and the refractive index satisfy the relation:
sin(i )
n
sin( r )
This is known as the Snell’s Law.
If there are two different media,
as shown in the figure, then
the Snell’s Law has the form:
sin( i ) n2

sin( r ) n1
i
r
Note that it is consistent with
the upper one. Suppose that
Medium 1 is vacuum; and,
obviously:
nvacuum
c
 1
c
So we indeed get the same
formula as the “upper” one.
Here is an animated example. A ray is incident from air on water surface. The
refractive index of air is 1.0003, so with a good approximation can be taken as 1.
For water, it is easy to remember: n = 4/3 = 1.3333.
We change the angle of incidence from 0 to 90º. The angle of refraction is
always smaller. What is its maximum value?
W e use t heSnell Law :
sin( i ) 4

sin( r ) 3
Recast it :
3
sin( r )  sin( i )
4
For  i  90 we get :
3
 0.75
4
Using a calculat or,
we find :
sin( r ) 
( r ) max  48.590
Now we want to consider, what happens, if light impinges
on the water surface, but “from below”.
Here The Principle of Ray Reversibility comes in handy:
Any actual ray of light in an optical system, if reversed
in direction, will retrace the same path backward
So, in theSnell Law we previouslyused we
simply replace i by  r , and vice versa,
sin( r )
4
to obtain:
n
sin( i )
3
4
or : sin( r )  sin( i )
3
4
sin( r )  sin( i )
3
The maximum value sin(θr) can take is 1.
It happens when sin(θi) = ¾ = 0.75, it is,
when θi = 48.59º
θi = 48.59º in the present
case is the critical angle.
For θi larger than the critical angle the Snell Law
is no longer valid!
For θi > 48.59º, light incident “from below” on water surface is no longer
refracted, but totally reflected – this effect is
called a total internal
reflection of light.
Here is the same animation, but
a slower one:
Let’s discuss: a diver underwater looks up – what does she see?