Transcript 30._ReflectionAndRefraction

Part V. Optics
30. Reflection & Refraction
31. Images & Optical Instruments
32. Interference & Diffraction
Drops of dew act as miniature optical systems,
with light refracting through the drops to form myriad images of the background flowers
－which themselves are out of focus in the photographer’s camera.
30. Reflection & Refraction
1.
2.
3.
4.
Reflection
Refraction
Total Internal Reflection
Dispersion
Why does the bee’s image appear at left,
and what does this have to do with e-mail and the Internet?
Ans: Total internal reflection; fibre optics.
30.1. Reflection
Conductor: E of light drives e to oscillate
 re-radiate
 reflection
Huygens-Fresnel principle :
Each point of an advancing wave front is the source of new (spherical) waves.
The new wave front is tangent to all these waves.
angle of incidence = angle of reflection
 = 
Specular reflection
( smooth surface )
Diffuse reflection
( rough surface )
Example 30.1. The Corner Reflector
Two mirrors join at right angles.
Show that any light ray incident in the plane of the page
will return anti-parallel to its incident direction.
Ray turned by
angle B here
Ray turned by
angle A here
A  2
A  B  180
Partial Reflection
Continuity of fields at boundary
 incident waves always partly reflected.
Least reflection at normal incidence (4% for glass).
Anti-reflection coating for lens, solar cells…
30.2. Refraction
Wave speeds differ in different media.
c
n
v
index of
refraction
Observers at A & B count same number of wave crests at any given duration
 wave frequency doesn’t change in crossing media.
v
c
 
f n f
  smaller for medium with slower v or higher n.
Table 30.1. Indices of Refraction
 1   1
1
1
2
c
v
n

n 1 sin  1  n 2 sin  2
v1 t
v t
 2
sin  1 sin  2
Snell’s law
Example 30.2. Plane Slab
A light ray propagating in air strikes a glass slab of thickness d and refractive
index n at incidence angle 1.
Show that it emerges from the stab propagating parallel to the original direction.
At 1st (upper) interface
sin  1  n sin  2
At 2nd (lower) interface
n sin  3  sin  4
Since
 3  2
 1  4
Example 30.3. CD Music
The laser beam that reads information from a compact disc is 0.737 mm wide
when it strikes the disc, and it forms a cone with half angle 1 = 27.0.
It then passes through a 1.20 mm thick layer of plastic with refractive index
1.55 before reaching the reflective information layer near the disc’s top surface.
What is the beam diameter d at the information layer?
At the incidence (lower) interface:
sin  1  n sin  2
At the information (upper) surface:
d  D  2 x  D  2 t tan 2
 1 sin 27.0 
 0.737 mm  2  1.2 mm  tan  sin

1.55


 0.00180 mm  1.80 m
GOT IT? 30.1.
The figure shows the path of a light ray through three different media. Rank the
media according to their refractive indices.
n3 > n1 > n2
Multiple & Continuous Refraction
Air’s temperature-dependent refractive index results
in the shimmering mirages you see on highways.
What you’re actually seeing is refracted sky light.
Refraction, Reflection, & Polarization
Incident beam with in-plane polarization:
no reflection when
refr = p  Brewster (or polarizing) angle
 refr   p  90
( reflected beam longitudinal: not EM )l
n1 sin  p  n2 sin  refr  n2 sin  90   p   n2 cos  p
n2
tan  p 
n1
p  56 for air-glass
Reflected light is perpendicularly polarized if incidence is at p .
30.3. Total Internal Reflection
Critical angle c for total internal reflection ( refr  90 )
n1 sin  c  n2
n1 > n2
Example 30.4. Whale Watch
Planeloads of whale watchers fly over the ocean.
Within what range of viewing angles can the whale see the planes?
1
sin  c 
1.333
 c  48.6
The whale sees the entire world above the surface in a cone of half-angle θc ;
beyond that, it sees reflections of objects below the surface.
GOT IT? 30.2.
The glass prism in figure has n = 1.5 and is surrounded by air ( n = 1 ).
What would happen the the incident light ray if the prism is imersed in
water ( n = 1.333 )?
Beam is both reflected & refracted at the
diagonal interface .
Application: Optical Fibre
Typical fibre: glass core of d = 8 m,
cladded by smaller n glass.
total internal reflection
Typical transmission ~ km.
SemiC laser:  = 850, 1350, 1550 nm
Required bandwidths:
Audio:
kHz
TV:
6 Mhz
Microwave freq: 1010 Hz
Light freq:
1014 Hz
30.4. Dispersion
v depends on   n depends on  : dispersion
Dispersion separates the colors in white light, with
shorter-wavelength violet experiencing the greatest
refraction.
Rainbow
Double rainbow and supernumerary rainbows on the inside of the
primary arc. The shadow of the photographer's head marks the centre
of the rainbow circle (antisolar point).
The rainbow is a circular arc located at 42 ° from
the line that connects the Sun, the observer, and
the center of the arc.
The primary rainbow results from total
reflection in raindrops that concentrates
light at approximately 42° deflection.
Dispersion separates wavelengths slightly,
resulting in the rainbow’s colors.
Light rays enter a raindrop from
one direction (typically a straight
line from the Sun), reflect off the
back of the raindrop, and fan out
as they leave the raindrop. The
light leaving the rainbow is spread
over a wide angle, with a
maximum intensity at 40.89–42°.
White light separates into different
colours on entering the raindrop
because red light is refracted by a
lesser angle than blue light. On
leaving the raindrop, the red rays
have turned through a smaller
angle than the blue rays, producing
a rainbow.
The spectrum of a diffuse gas－here
hydrogen－consists of light at discrete
wavelengths.
Glass lenses:
chromatic aberration.
Varying ionization level in ionosphere
 dispersion in radio waves
Comparing travel times of radio waves of different freq reveals
atmospheric conditions
 dual-freq GPS with cm resolution