http://www.phys.pe.kr/03_wave/03_wave_menu.html
reflection & refraction of light
PHY232
Remco Zegers
zegers@nscl.msu.edu
Room W109 – cyclotron building
http://www.nscl.msu.edu/~zegers/phy232.html
quiz (extra credit)
¾ which of the following is not correct in case of an AC LRC
circuit?
a) in case the inductive (XL) and capacitive reactances
(XC) are equal in size, the rms current through the circuit
is largest.
b) The current through and voltage over the resistor are in
always in phase
c) if the LRC circuit is in resonance, both the capacitive
reactance and inductive reactance must be zero
d) the rms current at resonance (I.e. when it is largest) is
independent of the frequency.
PHY232 - Remco Zegers reflection & refraction of light
2
light
¾ c=fλ
¾ light: wavelike oscillation of E and B fields (just like any
electromagnetic radiation). The only things special about
it, is that we can see it.
PHY232 - Remco Zegers reflection & refraction of light
3
light rays and wave-front
wavefront
rays
¾ isotropic light source (uniform in all directions):
¾ the wavefronts indicate maxima in the E/B oscillations
¾ the rays indicate the direction of the wave fronts
¾ I=Psource/(4πR2) I: intensity (W/m2) Psource :power of
source. R distance from source
PHY232 - Remco Zegers reflection & refraction of light
4
Huygens principle
¾ All points on a wavefront serve
as point sources of spherical
secondary wavelets. After a
time t, the new positions of the
wavefront will be the tangent of
these secondary wavelets
motion of a plane wave:
vt2
vt1
t=0
PHY232 - Remco Zegers reflection & refraction of light
5
Huygens principle II
¾ For a circular wavefront…
vt2
vt1
t=0
PHY232 - Remco Zegers reflection & refraction of light
6
question
¾ consider a square wavefront at t=0. After some time, the wavefront
has traveled outward and is now shaped like a
¾ a) circle
¾ b) square
¾ c) ellipse
¾ d) rounded square
PHY232 - Remco Zegers reflection & refraction of light
7
from now on…
¾ we usually only draw the light rays and not the wave-front
PHY232 - Remco Zegers reflection & refraction of light
8
reflection
¾ consider a light ray that
strikes a mirror. It will be
reflected.
¾ The angle of incidence
(relative to the normal to
the plane) equals the
the angle of reflection
¾ r=I
normal
i r
mirror
¾ of course, the mirror
must be very flat for this
to be true
PHY232 - Remco Zegers reflection & refraction of light
9
virtual image
¾ if we look at a mirror,
we see an image at a
location where the
object not really is.
¾ the image is formed at
a location where there
is not light present
¾ this is called a virtual
image
¾ see next chapter…
PHY232 - Remco Zegers reflection & refraction of light
10
index of refraction and speed of light
¾ In vacuum, the speed of light equals c=3x108 m/s.
¾ In any other medium, light propagates more slowly..
¾ in air: v=c/1.0003
¾ in water: v=c/1.33
¾ in glass: v=c/1.5
¾ in general: v=c/n
where n: index of refraction
¾ n also depends on the wavelength (λ)
n is larger for smaller λ
this effect is called dispersion
PHY232 - Remco Zegers reflection & refraction of light
11
refraction
¾ if light passes from one medium with refractive index n1 to
a medium with refractive index n2 it is bent (refracted):
¾ Snell’s law
n1sinθ1=n2sinθ2 or n1/n2=sinθ2/sinθ1
PHY232 - Remco Zegers reflection & refraction of light
12
refraction II
¾ if n1< n2 then the light ray
bends towards the normal
when passing through the
medium
¾ if n1> n2 then the light ray
bends away from the
normal when passing
through the material.
PHY232 - Remco Zegers reflection & refraction of light
13
demo
¾ consider a light ray traveling from
air to water at an incident angle of
300. Given nwater=1.33, what is the
angle of refraction?
θ2=sin-1(n1sinθ1/n2)
=sin-1(1xsin300/1.33)=
= 22.080
¾ Now, consider the light-ray
traveling from water to air at the
same incident angle. What is the
angle of refraction?
n1/n2=sinθ2/sinθ1
θ2=sin-1(n1sinθ1/n2)
=sin-1(1.33xsin300/1.)=
= 41.60
PHY232 - Remco Zegers reflection & refraction of light
14
question
¾ a light ray hits a 1 cm glass plate (n=1.5) at an incident
angle of 300. The light emerges from the glass plate at an
angle
θ=300
¾ a) <300
¾ b) =300
¾ c) >300
at air-glass interface:
θ2=sin-1(n1sinθ1/n2)=sin-1(1xsin300/1.5)= 19.470
at glass-air interface
θ2=sin-1(n1sinθ1/n2)=sin-1(1.5xsin19.470/1.)= 300
θ=???
http://www.phys.pe.kr/bbs/view.php?id=wave&page=1&sn1=&divpage=1&category=3&sn=off&ss=on&sc=on&select_arrange=headnum&desc=asc&no=11
PHY232 - Remco Zegers reflection & refraction of light
15
question: harpoon fishing
¾ You are standing on the shore near a lake and see a fish
in the water which you want to spear. Should you aim the
spear a) directly at the fish, b) just above it or c) just under
it?
answer c)
a
b
c
PHY232 - Remco Zegers reflection & refraction of light
16
a harpoon fisher
¾
http://www.phys.pe.kr/bbs/view.php?id=wave&page=1&sn1=&divpage=1&category=3&sn=off&ss=on&sc=on&select_arrange=headnum&desc=asc&no=2
PHY232 - Remco Zegers reflection & refraction of light
17
total internal reflection
¾ consider a ray of light traveling from
water to air.
¾ since nwater > nair a light ray is bent away
from the normal
θ2=sin-1(nwatersinθ1/nair)
¾ however, if
nwatersinθ1/nair>1
sinθ1>nair/nwater
θ1>sin-1(nair/nwater)
θ1>48.7o
…this equation has no solution,
since sinθ cannot be larger than 1
PHY232 - Remco Zegers reflection & refraction of light
18
internal reflection II
¾ when traveling from a medium 1 to a medium 2 with
n1>n2:
if sinθI>n2/n1 refraction is not possible and all light will be
reflected; θ=sin-1(n2/n1) is called the critical angle
PHY232 - Remco Zegers reflection & refraction of light
19
transport of light!
demo
PHY232 - Remco Zegers reflection & refraction of light
20
question
θ=500
¾ given the above situation and the fact that the critical
angle for water->air is 48.70, would the harpoonist know
where to aim at? I.e. does she see the fish?
a) yes
b) no
PHY232 - Remco Zegers reflection & refraction of light
21
dispersion
¾ we already saw that the index of refraction depends on
the wavelength (I.e. color) of the light.
¾ this can be used to separate white light into its component
colors.
demo
PHY232 - Remco Zegers reflection & refraction of light
22
rainbow
¾ depending on the location of
the raindrop and the angle a
person is looking at it, only light
of a certain wavelength (color)
is visible.
¾ The angle (location) changes
depending on where the drop
is, so that one sees different
colors at different locations in
the sky…
PHY232 - Remco Zegers reflection & refraction of light
23
lon-capa
¾ after reviewing this lecture, do questions 1-6 from HW set
8.
¾ to do these problems: be careful with what is the initial
and final medium…
PHY232 - Remco Zegers reflection & refraction of light
24