OpticsMirrors and Lenses

The Principle of Reflection

The Angle of Incidence = The Angle of Reflection

Reflection• We describe the path of light as straight-line rays• Reflection off a flat surface follows a simple rule:

angle of incidence equals angle of reflection angles measured from surface “normal line” (perpendicular)

normal line

sameangleincident ray exit ray

reflected ray

Reflection

• Virtual Image

–“Not Real” because it cannot be projected

–Image only seems to be there!

Mirror Image

Image formation from a plane mirror

Image appears at adistance equal to theobject distance.

Image is the samesize as the object.

Virtual Images in Plane Mirrors  

If light energy doesn't flow from the image, the image is "virtual".

Rays seem to come from behindthe mirror, but, of course, theydon't.  It is virtually as if the rayswere coming from behind the mirror.

"Virtually":  the same as if

As far as the eye-brain system isconcerned, the effect is the sameas would occur if the mirror wereabsent and the chess piece were actually located at the spot labeled "virtual image".

Hall Mirror• Useful to think in terms of images

“image” you

“real” you

mirror onlyneeds to be half as

high as you are tall. Yourimage will be twice as far from you

as the mirror.

LEFT- RIGHT REVERSAL

AMBULANCE

Refraction

The bending of light upon entering a medium withwith a different density.

A light wave will speed up or slow down in response to a

changing medium.

Beach Party

Imagine lines of people rushing from the parking lot to the sandy beach. People can run faster on pavement than in the sand.

Pavement

Sand

Beach Party

Pavement

Sand

Beach Party

Pavement

Sand

Beach Party

Pavement

Sand

Beach Party

As people enter the sand, they slow down.

Pavement

Sand

Beach Party

Pavement

Sand

Beach Party

Pavement

Sand

Refraction

Light waves, like people waves, will slow down and bend or refract.

Refraction

As a wave enters a piece of glass its velocity slows down and the wave is bent towards the normal line. As it exits it will speed up and is bent away from the normal line.

Air

Glass medium

Surface Normal

IncidentAngle

Dispersion

Light of different frequencies is refracted by different amounts

Red Light (lower frequency, longer wavelengths) is bent the least.

Blue Light (higher frequency, shorter wavelengths) is bent the

most.

Refraction is Dispersive

The Beauty of Dispersion and Refraction

Rainbows

Reflection• Real Image

–Image is made from “real” light rays that converge at a real focal point forming a REAL intersection of light.

–Can be projected onto a screen because light actually passes through the point where the image appears

–Always inverted

Curved mirrors

• What if the mirror isn’t flat?– light still follows the same rules, with local surface

normal• Parabolic mirrors have exact focus

– used in telescopes, backyard satellite dishes, etc.– also forms virtual image

Concave Mirrors•Curves inward•May be real or virtual image

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Convex Mirrors

•Curves outward•Reduces images•Virtual images

–Use: Rear view mirrors, store security…

CAUTION! Objects are closer than they appear!

For a real object between f and the mirror, a virtual image is formed behind the mirror. The position of the image is found by tracing the reflected rays back behind the mirror to where they meet. The image is upright and larger than the object.

For a real object close to the mirror but outside of the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object.

For a real object between C and f, a real image is formed outside of C. The image is inverted and larger than the object.

For a real object between C and f, a real image is formed outside of C. The image is inverted and larger than the object.

For a real object between f and the mirror, a virtual image is formed behind the mirror. The position of the image is found by tracing the reflected rays back behind the mirror to where they meet. The image is upright and larger than the object.

For a real object close to the mirror but outside of the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object.

For a real object between C and f, a real image is formed outside of C. The image is inverted and larger than the object.

For a real object at C, the real image is formed at C. The image is inverted and the same size as the object.

For a real object at C, the real image is formed at C. The image is inverted and the same size as the object.

For a real object between f and the mirror, a virtual image is formed behind the mirror. The position of the image is found by tracing the reflected rays back behind the mirror to where they meet. The image is upright and larger than the object.

For a real object close to the mirror but outside of the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object.

For a real object close to the mirror but outside of the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object.

For a real object at f, no image is formed. The reflected rays are parallel and never converge.

For a real object at f, no image is formed. The reflected rays are parallel and never converge.

What size image is formed if the real object is placed at the focal point f?

For a real object between f and the mirror, a virtual image is formed behind the mirror. The image is upright and larger than the object.

For a real object between f and the mirror, a virtual image is formed behind the mirror. The position of the image is found by tracing the reflected rays back behind the mirror to where they meet. The image is upright and larger than the object.

Refraction• Light also goes through some things

– glass, water, eyeball, air• The presence of material slows light’s progress

– interactions with electrical properties of atoms• The “light slowing factor” is called the index of

refraction– glass has n = 1.52, meaning that light travels about 1.5

times slower in glass than in vacuum– water has n = 1.33– air has n = 1.00028– vacuum is n = 1.00000 (speed of light at full capacity)

n2 = 1.5

n1 = 1.0

A

B

Refraction at a plane surface• Light bends at interface between refractive

indices– bends more the larger the difference in refractive

index

Convex Lenses

Thicker in the center than edges. – Lens that converges

(brings together) light rays.

– Forms real images and virtual images depending on position of the object

The Magnifier

Concave Lenses

• Lenses that are thicker at the edges and thinner in the center. – Diverges light rays – All images are

erect and reduced.The De-Magnifier

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Let’s get focused…• Just as with mirrors, curved lenses follow same

rules using the optical axis and focal point.A lens, with front and back curved surfaces, bends light twice, each diverting incoming ray towards

the focal point.Light rays follow the laws of refraction

at each surface.

Parallel rays, coming, for instance from a specific direction are focused

by a convex lens to a focal point.

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Cameras, in brief

In a pinhole camera, the hole is so small that light hitting any particular pointon the film plane must have come from a particular direction outside the camera

In a camera with a lens, the same applies: that a point on the film planemore-or-less corresponds to a direction outside the camera. Lenses havethe important advantage of collecting more light than the pinhole admits

pinholeimage atfilm plane

object

image atfilm plane

object

lens

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The EyeNow for our cameras…The eye forms an image on the retina.

– The cornea does 80% of the work, with the lens providing slight tweaks (accommodation, or adjusting)

Refractive indices:air: 1.0cornea: 1.376fluid: 1.336lens: 1.396

Central field of view (called fovea)densely plastered with receptors forhigh resolution & acuity. Fovea is the focal point for the images.

How You See

• Near Sighted – Eyeball is too long and image focuses in front of the retina

• Near Sightedness – Concave lenses expand focal length

• Far Sighted – Eyeball is too short so image is focused behind the retina.

• Far Sightedness – Convex lense shortens the focal length.

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Bonus Questionsplace your answer on a index

card to turn in tomorrow.

1) Why can’t we focus our eyes under water?

2) Why do goggles help?