1. Part V. Optics Reflection & Refraction Images & Optical Instruments
Interference & Diffraction

2. 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.

3. 30. Reflection & Refraction
Total Internal Reflection
Dispersion

4. Why does the bee’s image appear at left,
and what does this have to do with and the Internet?
Ans: Total internal reflection; fibre optics.

5. 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  = 

6. Specular reflection
( smooth surface )
Diffuse reflection
( rough surface )

7. 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

8. 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…

9. 30.2. Refraction index of refraction
Wave speeds differ in different media.
Observers at A & B count same number of wave crests at any given duration
 wave frequency doesn’t change in crossing media.
  smaller for medium with slower v or higher n.

10. Table 30.1. Indices of Refraction

11. 1
1 2 
Snell’s law

12. Example 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
At 2nd (lower) interface
Since

13. Example CD Music
The laser beam that reads information from a compact disc is 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 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:
At the information (upper) surface:

14. GOT IT?
The figure shows the path of a light ray through three different media. Rank the media according to their refractive indices.
n3 > n1 > n2

15. 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.

16. Refraction, Reflection, & Polarization
Incident beam with in-plane polarization:
no reflection when
refr = p  Brewster (or polarizing) angle
( reflected beam longitudinal: not EM )l
p  56 for air-glass
Reflected light is perpendicularly polarized if incidence is at p .

17. 30.3. Total Internal Reflection
Critical angle c for total internal reflection ( refr  90 )
n1 > n2

18. Example Whale Watch
Planeloads of whale watchers fly over the ocean.
Within what range of viewing angles can the whale see the planes?
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.

19. GOT IT?
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 = )?
Beam is both reflected & refracted at the diagonal interface .

20. 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: Hz

21. 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.

22. 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).

23. 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.
The rainbow is a circular arc located at 42 ° from the line that connects the Sun, the observer, and the center of the arc.

24. 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.

25. Glass lenses: chromatic aberration.
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