Welcome to Physics 7C!Welcome to Physics 7C!

Lecture 9 -- Winter Quarter -- 2005

Professor Robin Erbacher

343 Phy/Geo

erbacher@physics.ucdavis.edu

AnnouncementsAnnouncements

• Quiz today on Block 14, DLMs 13-15.

• Block 15: Light, Optics, and Images.

• Lecture 10 will be a review for the final. Check website for TA review sessions on the 17th and 18th.

• Final Exam: Saturday March 19, 1:30-3:30 pm

• On final exam, you will be responsible for content in lectures as well as in DL. See Lecture 10.

• Turn off cell phones and pagers during lecture.

Rays of LightRays of LightSo far we have represented waves, including sound, and electromagnetic waves (light) using 1 dimension. Even withwaves that spread out-- wave fronts passing through slits-- we pick a direction and use 1 dimension.

When we discuss light waves and the way they diverge or converge in 2 and 3 dimensional space, we use wavefronts.

Wavefronts are concentric spheres in 3-d and lines in 2-d.

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A source of waves often sends out a wavefront in all directions, but many times we are interested only in one direction.

Then we draw rays!QuickTime™ and aTIFF (Uncompressed) decompressor

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Law of ReflectionLaw of ReflectionJust as in our generic 1-d wave model, when light hits a boundary with a different “impedance”, some of the energy is reflected and some is transmitted.

If the boundary is smooth on a scale smaller than a , we have specular relection: a mirror !

When the light ray comes in at an angle:

“The Law of Reflection”

€

θincident =θ reflection

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Impedances: Index of RefractionImpedances: Index of RefractionWhen light hits a medium with different “impedance”, the light either speeds up or slows down.

€

vlight in medium = cspeed of light in vacuum/nmedium

This impedance is called the Index of Refraction (n):

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Tractor wheelson soft grass…

Compare to Sound Waves!

The Law of RefractionThe Law of Refraction

Snell’s Law:

€

n1 sinθ1 = n2 sinθ2

If the light enters at an angle to the normal, as it passes from medium 1 having index n1 to medium 2 having index n2, the light rays will bend according to the Law of Refraction (Snell’s Law).

What’s the incident angle from the normal on the curve?

If the light rays are normal to the boundary, then no refraction.

Unless it’s “monochromatic”, light contains components in a range of wavelengths, corresponding to various visible colors.

Recall: v = f, where v is the velocity of the wave in a medium. We also know that for light, v = c/n, so that n = c/ f.

This means that light can be separated! Different wavelengths will experience different “impedence” or n, and according to Snell’s Law, will refract at different angles!

Spectrum of Light: PrismsSpectrum of Light: Prisms

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Aside: Why is the Sky Blue?Aside: Why is the Sky Blue?

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Sun has white light (many colors), but nitrogen and oxygen scatter short wavelengths more easily, the so-called BIV part of the spectrum.

In mid-day, the path through the atmosphere is smaller, so less scattering, and more of the yellows come through.

In the evening, path length is very large and the wavelengths that make it through are reds and oranges. The more particles, the better the sunset! (The more the polution.)

Sunset on Aitutaki, Cook Islands

Tricky SightsTricky Sights

What’s going on?We use ray traces to explain why the pencil looks broken!

Water, glass, or other media bend light like lenses.

Result: Things are not always how they appear!

Why doesn’t the fish look worried?

Total Internal ReflectionTotal Internal ReflectionWhen light passes from a more-dense (n1) to a less-dense (n2) medium, as the angle of incidence increases, the refracted ray in the

less dense medium bends more toward the normal until θ2=90o.

At this angle, called the critical angle θc, all of the light is internally reflected back into the medium.

The greater the difference between indices of refraction, the small the critical angle.

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sinθc = n2 n1

Example: Fiber Optics

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Example: Diamonds

θc=25o

rays

idealized

object

diffusely

reflecting

object

rays

ImagesImages

Whether through water or in a mirror, we often see images of objects in specific locations.

We can now calculate where we will see these images, and how big they will be.

object image

eye

Ray Traces!

Thin LensesThin LensesLenses bend rays twice: at the front and at the back. Thin lenses are idealized, so we only look at the net effect on rays.

Thin lens equation:

€

1

f=

1

o+

1

i

f 1

f 1

image 1

object 1

o i 1 1

f = focal length (+ converging, - diverging)o = object-to-lens (+ if object in front of lens)i = lens-to-image distance (can be +/-)

We can use ray traces or this equation to find both real and virtual images, as you will see in DL this week.

h h

o i

light

lens

o i

Magnification:

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M linear =hiho

= −i

o

⎛

⎝ ⎜

⎞

⎠ ⎟

A lens has a particular magnification: the image height to the object height.

OptometryOptometryThe ability of our eyes to change focus is called accommodation. Our ciliary muscles change the shape of our lenses. The farthest object you can see is the “far point” and should be at ∞. The closest point is the “near point”, and should be greater around 25 cm.

relaxed

lens

accomodated

lens

Presbyopia (elderly eyes) comes from the loss of accommodation with age, and happens to everyone. (Bi-focals!)Hyperopia comes from flat corneas, and myopia from over-curved corneas. relaxed lens

too curved

slightly accomodated

lens

Two lens systems:Contacts, plus eyes,Can often fix things.

You will practice with multiple lenses in DL.

i (fixed)

object

ciliary

muscles

lens (cornea and

crystalline lens)

o (variable)

image

on retina