physics 7c, lecture 3 winter quarter -- 2007 light rays, wavefronts, optics, lenses professor robin...

Physics 7C, Lecture 3Physics 7C, Lecture 3

Winter Quarter -- 2007Winter Quarter -- 2007

Light rays, Wavefronts, Optics, Lenses

Professor Robin Erbacher343 Phy/Geo

[email protected]

AnnouncementsAnnouncements

• Course syllabus (policy, philosophy) on the web: http://physics7.ucdavis.edu

• Quizzes every other lecture, ~20 minutes each, average of 4 best = 45% (or 20)% of grade.

• Final on Monday, March 19 10:30 am. If you cannot make this we suggest 7C in a different quarter.

• Quiz #2 today, see calendar on web. Quiz #1 results posted yesterday.

• Turn off cell phones and pagers during lecture.

http://physics7.ucdavis.edu/

WavefrontsWavefrontsSo far we have represented waves, including sound using 1 dimension. Even with waves that spread out-- wave fronts passing through slits-- we pick a direction and use 1 dimension. We will now also approximate electromagnetic waves (light) with a model in one dimension as well.

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.

•A wavefront represent points of equal phase (e.g. the crest of the wave).

•The ray shows the direction in which the wavefront is moving.

•Rays are perpendicular to wavefronts.

Circular, Spherical, Planar Circular, Spherical, Planar

Circular (2-d) and spherical (3-d) wavefronts can be approximated by plane waves (flat) for sufficiently small samples and large distances.

Rays of LightRays of Light

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

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

are needed to see this picture.QuickTime™ and a

TIFF (Uncompressed) decompressorare needed to see this picture.

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 reflection: a mirror !

When the light ray comes in at an angle:

“The Law of Reflection”

€

θincident =θ reflection

Law of ReflectionLaw of Reflection


are needed to see this picture.

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):



Tractor wheelson soft grass…

Compare to Sound Waves!

The Law of RefractionThe Law of RefractionSnell’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).

PRS Question:How are the light rays bent if they come innormal (perpendicular) to the boundary?a) The light rays will bend along the surface of the

boundary.b) The rays will reflect backward completely.c) The rays will refract (bend) 45° to the normal. d) The light will pass through the boundary unchanged.

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.

Mirages: Index of RefractionMirages: Index of Refraction

Refraction of light in the same medium: Temperature changes toward the ground causes the index of refraction to vary.

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



QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.



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







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.



€

sinθc = n2 n1

Example: Fiber Optics





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:

€

M linear =hiho

= −i

o

⎛

⎝ ⎜

⎞

⎠ ⎟

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

Convex LensesConvex Lenses• Similar to a pair of prisms with the tips on the top and bottom (D/L)• Bends parallel rays towards the axis.

Focal length

Concave LensesConcave Lenses• Similar to a pair of prisms with the tips near the axis where they meet.• Bends parallel rays away from the axis.

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.

Seeing the Light?Seeing the Light?What kind of wave is a light wave? It’s a transverse excitation, perpendicular to the direction of wave propagation.

What’s the medium that’s displaced as the wave propagates?

Nothing!

Light propagates via oscillating electric and magnetic fields! (more on this next week in Block 9…)

The Enigmatic Ether!

Light: Visible, and Invisible Light: Visible, and InvisibleThe light we see is a small portion of the radiation that exists!

Visible Light:4.3-7.5 x 1014 Hz

Ultra Violet (UV)X-rays/ rays

Infra Red IRwave, AM/FM, TV

frequency

wavelength

Light: Visible, and Invisible Light: Visible, and InvisibleThe light we see is a small portion of the radiation that exists! The light we see is a small portion of the radiation that exists!

Visible Light:4.3-7.5 x 1014 Hz

Ultra Violet (UV)X-rays/ rays

Infra Red IRwave, AM/FM, TV

frequency

wavelength

physics 7c, lecture 3 winter quarter -- 2007 light rays, wavefronts, optics, lenses professor robin...

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