physics 116 - university of washington · physics 116 lecture 19 rainbows, the ... the anti-solar...
TRANSCRIPT
•! Physics Study Centernow staffed by TAs an hour later on
M-W: 9:30 am to 6:30 pm M-W, 9:30am-5:30pm Th,
10:30am-5:30pm F.
•! The Royal Society (UK) made its journals free to public:
Take a look at Isaac Newton's 1671 paper on his
experiments with solar spectra using prisms. (Yes, that's
right: the pdf file says ”© 1671" ! )
•! Exam 2 one week from today: same procedures as last time
•! Practice exam posted Thursday, in class Friday
•! YOU bring bubble sheet, pencil, calculator
Announcements
3
Today
Lecture Schedule (up to exam 2)
4
Rainbows, Halos, etc
•! Rainbows come from the refraction of sunlight in round water droplets (round prisms)
–! preferred one-bounce reflection path has ~42° deflection angle
–! rainbow arc always centered on anti-solar point (opposite direction to sun)
–! different colors refract at slightly different angles, as in glass prism
•! Caused by differences in refractive index of water for different colors (wavelengths)
red appears higher in bow than blue single bounce; red & blue paths different
5
Questions
•! Which general direction will a rainbow be found in the evening?
•! Why don’t you see rainbows during the middle of the day?
–! You must have bright sunlight coming from behind you, illuminating rainfall in front of you
6
Rainbows come in pairs…
Secondary rainbow has two
reflections. Red now appears
lower than blue in the sky.
Higher orders cannot usually be seen. The primary bow is brighter, and the color sequence
is reversed in the much-fainter secondary.
Secondaries are best seen when rain is heavy while
sunlight coming from behind you is bright
•! Rainbows have multiple orders corresponding to number of reflections in raindrop: 2nd-order bow appears at 51 degrees:
7
Glorys and Heiligenschein (shadow-hiding)
•! A circular rainbow about the anti-solar direction is called a glory
–! Sometimes 2–3 colored rings
–! often see shadow in middle
–! water droplets must be very small (fog): more complicated optics than rainbow
•! The anti-solar point may also get bright due to reflection from dewdrops
–! called heiligenschein (holy-shine)
–! Similar effect when you look into murky water
–! Why is the halo always around your head’s shadow?
•! no, you are not an angel
The Eye
•! Now for our cameras…
•! Eye forms image on retina, where light is sensed by special cells
–! Cornea does 80% of the refracting work, with the lens providing slight tweaks (accommodation, or adjusting focus)
Refractive indices:
air: 1.0
cornea: 1.376
fluid: 1.336
lens: 1.396
Central field of view (called fovea)
densely plastered with receptors, for
high resolution & acuity.
Fovea only views a few degrees of the
center of your field of vision.
Human Vision
•! Parts of the eye:
1.! Iris: limits amount of light admitted
2.! Lens: focussing range = 25 cm (near pt) to ! (far pt)
•! myopia (nearsightedness): near, far pts are closer
•! hyperopia (farsightedness): near, far pts are farther
•! Presbyopia (“elderly eyes”): loss of lens elasticity
–! simultaneously near and farsighted!
–! bifocals needed
2
4
8 10
10 30 50
Near-point distance (inches)
vs age (years) myopia
hyperopia
eye lens retina
age
Near point = closest distance
at which you can read
Human Vision
1.! Retina: 1.3 x 108 receptors
•! Rods:
–! monochromatic, very sensitive (peak at !=507 nm)
–! not useful in bright light - night (scotopic) vision
“When all candles be out, all cats be grey!”
–! pigment=rhodopsin (vitamin A + protein)
•! Cones: 3 color pigments, 20% as sensitive as rods
–! not useful in dim light
•! “bleaching”: pigments consumed,
need few sec to recover
•! Fovea: small retinal area with high density of cones –! high resolution, high color discrimination
–! rest of eye = “peripheral vision”
•! Blind spot: no receptors where optic nerve enters
Stare fixedly for a minute at one of these pix,
then gaze at a piece of white paper, or the wall (or white screen coming up…)
Human eye: resolution (sharpness of vision)
•! Sensors on retina
–! total 1.3 x 108 receptors
•! Rods: monochromatic, highly sensitive
–! Night vision
•! Cones: trichromatic, less sensitive
–! spacing at fovea ~ 2.6 x 10-6 m
•! Resolution –! smallest resolvable separation ~ 6 microns
on retina (at fovea)
–! Eye lens has f = 25mm, so smallest resolved
angle = 0.006mm/25mm = 0.0002 radian
(= 2 mm separation, viewed from 10 m)
Resolution drops to ~0.1 rad (5 deg) in dim light (rod vision)
"!
6 #m
25 mm
cone 1 2 3 on off on
~6 #m
Minimum
distinguishable pattern:
2 bright spots close together, just span 3
cones
How many photons do we see ?
Human eye is an amazing photon detector
•! Sunny day (outdoors): –! 1015 photons per second enter eye (2 mm pupil)
•! Moonlit night (outdoors):
–! 5!1010 photons/sec (6 mm pupil)
•! Moonless night (clear, starry sky) –! 108 photons/sec (6 mm pupil)
•! Light from dimmest star visible to naked eye (mag 6.5):
–! ~1000 photons/sec entering eye
–! “Exposure time” of retina cells is about 1/8 sec ! ~100 photons are enough to get a signal to the brain
What do we see?
•! Our eyes can’t detect light emitted from objects (mostly infrared), unless they get “red hot” or hotter
•! Light we see is from the sun or from artificial light –! Sunlight, home lighting, street lights
–! Phosphorescence, luminescence = light from chemical reactions in plants or animals
•! When we see objects, we see reflected light –! immediate bouncing of incident light (zero time delay)
•! Very occasionally we see light that has been absorbed,
then re-emitted at a different wavelength –! called fluorescence
–! Time delay, but just a tiny fraction of a second
Human eye as an optical instrument
•! Normal focusing range: 25 cm to infinity
•! Cornea + Lens focus light on retina: •! only 10% zoom due to lens contraction (+ 2mm in f)
•! Pupil limits light intensity (like iris on camera):
–! Opening varies from 2 mm to 6 mm (factor of 3)
•!Can’t control intensities much
–! Camera lenses are rated by “f-number” = f / diameter
•! so human eye “speed” is f#=(16mm/6mm)= f:3
•! Cats have f:1 eyes
–! We can view direct sun (briefly!) and also see stars down to 7th-magnitude with the naked eye
17
How does a magnifying glass work?
•! Light rays from object are refracted by lens to form a virtual image, apparently behind the lens
–! Virtual means you can view it by looking through the lens, but the light rays do not actually converge there (cannot catch it on film)
•! Light rays 1 and 2 appear to come from a bigger arrow located behind the real one: magnified
•! Must place object close behind lens (within focal length f)
•! Magnified image is really an optical illusion!
o
image
object f 2
1
18
Telescopes
•! Telescopes do 2 things: –! collect a lot of light across a big aperture
(opening) and cram this light into your eye
•! Lets you see fainter objects
–! magnify angles by ratio of the focal lengths of the main lens/mirror and eyepiece: Magnification=F/f
•! So object looks bigger to you
•! Simple operation –! Objective lens forms real image of object
inside telescope tube
–! Eye lens is used as magnifier to view real image made by objective
•! Come in two basic varieties: –! refractors, dating back to Galileo’s time
(objective = lens)
•! Galilean telescope: negative eyelens
–! Reflectors (mirror), invented by Newton!
–! all big telescopes now are reflectors
•! Only one surface to grind and polish
•! Easier to make in large sizes Newtonian
Reflector
Refractor