1. q q A B R O F f Refractive spherical surface Index n q/n b b = q - q/n
b = h/f
b = q - q/n = (h/R)(1-1/n)
n - 1
f R n =
( )
F = focus if position independent of h

2. q q A B f R O F Index n q x n b b = q (n-1) b = h/f
b = q (n-1) = (n-1)h/R
n - 1
( ) =
f R

3. The marvels of water drops and water crystals
Responsible for rain, snow, rainbows, Halo and glory
Measuring water droplets
Glory
Rainbow
The concept of “maximum deviation”
Halo
The concept of “minimum deviation”

4. How to monitor the size of a water droplet
as it growth or evaporates?
Through whispering gallery modes

5. H. C. Bryant and N. Jarmie, “The {Glory}",
Scientific American, 231:60—71 (1974)
Other application: monitoring the growth of
water drops in clouds (more spaced resonances)
Monitoring the evaporation of a large droplet
The successive narrow peaks are separated by 1/100 wavelengths,
indicating that they correspond to resonances of 100 cycles.
Backscattered
intensity
TIME

6. The Glory
A complete description of the glory involves not only the whispering gallery resonance,
but also the fact that the backscattering is issued from multiple light »rings«
(the annular edge of the droplets), which interfere with each other.
Simulation:
Make negative

8. Rainbow
The concept of “maximum deviation”

9. What happens to a narrow beam irradiating a water sphere?
Maximum deviation angle
The retro-refraction angle varies from zero to a limit angle qlim

10. Maximum intensity around the maximum deviation
Irradiation by an
extended beam
Maximum intensity around the maximum deviation
angle.

12. Double rainbow

15. The Halo
Related to the minimum deviation of water crystals

17. y = ax2 Parabola: curve at equal distance from a point (F) and line F

18. Parabolic mirror: why do all rays perpendicular to the directrix
converge at the focus F? F
y=2ax A x O x 2 C d D E

19. Off-axis parabolic mirror