Physics 1230: Light and Color · 2009-02-13 · transmission but only reflection for certain wavelengths. ... mirror movie awesome-mirror-prank . ... real chin is in front of the

Physics 1230: Light and Color

TOPIC 4 Geometrical optics - how do we make images? Ray tracing for mirrors (spotlights, Maglites, auto mirrors, make-up and shaving mirrors, globes, etc.)

http://www.colorado.edu/physics/phys1230

Mirrors

•  Lots of different kinds - Shaving mirrors Make-up mirrors Rear and side view mirrors Globes

• Unlike flat mirrors, some of the above mirrors make the image bigger while others make the image smaller

•  In some cases what you see depends on how close you are to the mirror

Materials like metals with many mobile electrons can cancel out the light wave field in the forward direction so there is no

transmission but only reflection for certain wavelengths.

•  Metals reflect all waves below a certain frequency –  the plasma frequency - which

varies from metal to metal •  Silver is particularly

interesting because it reflects light waves at all visible frequencies –  Its plasma frequency is at the

top of the violet so it reflects all of the wavelengths below and appears whitish

•  Gold and copper have a yellowish-brownish color because they reflect greens, yellows and reds but not blues or violets –  Red and green make yellow

What is a mirror? •  Since silver is such a good

reflector, a coating of silver on glass makes a good (common) mirror.

•  If the silver coating is thin enough the mirror can be made to transmit 50% of the light and to reflect the other 50% –  This is called a half-

silvered mirror –  A half-silvered mirror

used with proper lighting can show objects on one side or the other of the mirror

One-way Mirror: needs the correct lighting!

http://micro.magnet.fsu.edu/primer/lightandcolor/mirrorsintro.html

FLAT or PLANE Mirrors - Surface of mirror is flat

We interpret all rays coming into our eye as traveling from a fictitious image in a straight line to our eye even if they are reflected rays!

http://micro.magnet.fsu.edu/primer/lightandcolor/mirrorsintro.html

History of Mirrors

Predating even crude lenses, mirrors are perhaps the oldest optical element utilized by man to harness the power of light. Prehistoric cave dwellers were no doubt mesmerized by their reflections in undisturbed ponds and other bodies of water, but the earliest man-made mirrors were not discovered until Egyptian pyramidal artifacts dating back to around 1900 BC were examined. Mirrors made during the Greco-Roman period and the Middle Ages consisted of highly polished metals, such as bronze, tin, or silver, fashioned into slightly convex disks, which served mankind for over a millennium.

Archimedes’ Death Ray (Syracuse ca. 213 BC)

At last in an incredible manner he [Archimedes] burned up the whole Roman fleet. For by tilting a kind of mirror toward the sun he concentrated the sun's beam upon it; and owing to the thickness and smoothness of the mirror he ignited the air from this beam and kindled a great flame, the whole of which he directed upon the ships that lay at anchor in the path of the fire, until he consumed them all.

History of Mirrors

It was not until the late Twelfth or early Thirteenth Centuries that the use of glass with a metallic backing was developed to produce looking glasses, but refinement of this technique took an additional several hundred years. By the sixteenth century, Venetian craftsmen were fabricating handsome mirrors fashioned from a sheet of flat glass coated with a thin layer of mercury-tin amalgam. Over the next few hundred years, German and French specialists developed mirror-making into a fine art, and exquisitely crafted mirrors decorated the halls, dining, living, and bedrooms of the European aristocracy.

CURVED MIRROR REFLECTION AND IMAGES

•  Is there a difference between the reflection of yourself in a shaving/make-up mirror, or a corner viewing mirror, or your reflection in a round ornament?

•  What kind of mirror directs your car headlights, or a maglite beam, forward?

•  What kind of mirrors are used in very large telescopes?

CONCEPT QUESTION

In your make-up/shaving mirror, your image is -

A)  Smaller

B)  Bigger

C)  Same size

D)  Upside down

CONCEPT QUESTION

In a globe ornament, your image is -

A)  Smaller

B)  Bigger

C)  Same size

CONCEPT QUESTION

Compared to your own size, your reflection from a pond is -

A)  Smaller

B)  Bigger

C)  Same size

D)  More flattering

mirror movie

http://www.rofl.to/awesome-mirror-prank

mountain reflection

LAW OF REFLECTION

Angle of Incidence = Angle of Reflection

normal to surface

glass or metal

ϑi ϑr

LAW OF REFLECTION

Angle of Incidence = Angle of Reflection

normal to surface

ϑi ϑr

glass or metal

Making Images - definitions

•  OBJECT: This is the thing you see an image of.

•  VIRTUAL IMAGE:�� This is an image formed in a different place other than where the light is coming from. If you reach out to try to touch the image, your hand would hit the lens or mirror and not be able to touch the image. It is your psychological impression of where something is.

•  REAL IMAGE: This is an image formed in the air between you and the mirror or lens. You can stick your hand through this ghost-like image or see it on a screen.

•  Demonstrations

How is an image produced in a mirror? The meaning of a virtual image

•  If we trace rays for every ray from every part of Alex which reflects in the mirror

–  we get a virtual image of the real Alex behind the mirror. It is virtual because there is no light energy there, no real rays reach it, and it cannot be seen by putting a screen at its position!!

•  When all of the reflected rays from Alex's chin are traced backwards they all appear to come from the virtual image of his chin

–  Hence Alex's image is always in the same place regardless of where Bob looks

•  The image chin is behind the mirror by a distance = to the distance the real chin is in front of the mirror

–  This is true for all parts of Alex's image

–  Alex's virtual image is the same size as the real Alex

–  Alex's image is further away from Bob than the real Alex

Virtual image of Alex is behind the mirror

Mirror

Alex Bob looks at Alex's image

Bob sees Alex's image in the same place

wherever he moves his head

For simple (flat) mirrors the image location is therefore predictable without knowing where the

observer's eye is and without ray-tracing

Mirror

Mirror Mirror

Mirror

Spherical Mirrors

• Spherical mirrors appear to be cut from a section of a sphere. They can be concave or convex

• Each obeys the law of reflection

• BUT each kind of mirror makes a different kind of image

convex concave

Definitions for Spherical Mirrors •  Radius of Curvature: The radius of the sphere the mirror is “cut from”

•  Center of Curvature: The center of the sphere the mirror is cut from

•  Focal Point: The point where rays from a distance appear to converge

•  Focal Distance: The distance of the focal point from the mirror

•  Paraxial Ray: A ray coming on to the mirror parallel to the axis

paraxial ray

concave

center of curvature (C) focal point (F)

axis C F

convex

radius of curvature

axis C F

focal point (F)

paraxial ray

How do rays behave at spherical mirrors? •  We already know that “angle of incidence = angle of reflection”

•  However, this would take a lot of time if we tried to apply it to every ray

•  Instead we use the following “rules” for curved mirrors

•  RULE #1: All rays parallel to the axis are reflected such that they appear to come from the focal point F (notice that a ray coming in along a radius will have zero angle with respect to the normal, and so will be reflected back on itself)

How do rays behave at spherical mirrors? •  RULE #1: All rays parallel to the axis are reflected such that they appear to come from the focal point F

convex concave

. C C F F

How do rays behave at spherical mirrors? •  RULE #2: Incident rays coming towards the center of curvature are reflected back on themselves. Why?

convex concave

C C .

concave mirror

How do rays behave at spherical mirrors? •  RULE #3: Incident rays headed for F are reflected so that they are parallel to the axis.

(notice that this rule is just the reverse of Rule #1)

convex concave

C C F F

How do we make images using spherical mirrors?

Images in convex mirrors

•  RULE #1: All rays parallel to the axis are reflected such that they appear to come from the focal point F

•  RULE #2: Incident rays coming towards the center of curvature are reflected back on themselves

•  RULE #3: Incident rays headed for F are reflected so that they are parallel to the axis.

Another rule: parallel light rays

•  All parallel light rays coming in to a concave focusing mirror will be brought to a focus in a plane that includes the focal point. • Note that this rule applies to rays that are parallel to themselves – they do not have to be parallel to the axis.


Images in convex mirrors




Where is the focal point F for a curved mirror?

•  The focal point F is at half the distance from the mirror to the radius of curvature C on the main axis •  This can be seen to be approximately correct from the law of reflection. It is also proved in Appendix C of the textbook.





Images in concave mirrors

Concept question: How would you draw in other rays e.g. purple rays?

A.  By drawing them close to the existing rays

B.  Using the law of reflection

C.  Using a different rule







Spherical Mirror Simulations

Applet on Concave Mirrors

http://micro.magnet.fsu.edu/primer/java/mirrors/concavemirrors/index.html

Applet on Convex Mirrors

http://micro.magnet.fsu.edu/primer/java/mirrors/convexmirrors/index.html

Concept Question

Is your make-up/shaving mirror -

A)   Flat

B)   Concave

C)  Convex

Collecting radiation using parabolic reflectors

radar transmitter

radio telescope

headlamp

parabolic microphone

Parabolic mirrors as solar concentrators

parabolic trough

parabolic dish array

superheated steam generation

How does your car switch between high and low beams?

radar transmitter

Physics 1230: Light and Color · 2009-02-13 · transmission but only reflection for certain wavelengths. ... mirror movie awesome-mirror-prank . ... real chin is in front of the

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