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Geometrical Optics

  • B4-21: DEFLECTION OF BEAM - OPTICAL LEVER

    B4-21
    Demonstrate the small deflection of an aluminum beam due to weighting between supports.
    A mirror serves as an optical lever for the laser beam, with its fixed support legs on a lab jack and its other legs on the aluminum beam. The aluminum beam deflects as weights are added, causing the laser beam to move along the scale at the rear of the photograph.
    OS1, F1, ME1, LS1

    b4-21a b4-21b

  • E2-02: MEASUREMENT OF RADIUS OF EARTH

    E2-02
    Demonstrate how the radius of the earth can be measured using trigonometry.

    A disc of radius R with two radial tabs, as shown, is mounted on the optical board and illuminated by a parallel beam of light, as if the earth were being illuminated by the sun. The equatorial tab must have its shadow along the horizontal diameter of the disc. Measure the length b of the upper tab, the length a of its shadow, and the distance S along the surface between the two tabs. By geometry: S/R=a/b, or R=bS/a. Compare the result of this calculation with the direct measurement of the radius R of the disc.

    E2, ofc

    e2-02

  • E2-21: PHASES OF THE MOON

    E2-21
    Show the relationship between the phases of the moon and the relative earth-sun-moon positions.
    With the lecture hall dark, a point source illuminates the globe (the slated sphere from A1 is recommended) from various positions. Phases from crescent to full moon show up very clearly.
    A2, LS1

  • E2-22 UMBRA AND PENUMBRA

    E2-22
    Illustrates shadow umbra and penumbra
    The foam ball casts a shadow of each of the two point sources in the box. The umbra is where the two shadows overlap and the penumbra is where only one source is shadowed.
    E2, LS1

    E2-22A

  • E2-23: UMBRA AND PENUMBRA - EXTENDED SOURCE

    E2-23
    Show umbra and penumbra with an extended source, as in an eclipse.
    Hold the foam ball between the extended source (an incandescent-based television lightbox) and a projection screen (In the lecture halls, use the whiteboard behind the blackboards.). The shadow will consist of three distinct regions: (1) The umbra, in which all of the source is shadowed, is the dark central part. (2) The penumbra, where part of the source is shadowed, is the intermediate band around the umbra. (3) The outer region, where none of the source is shadowed, is the brightest region.
    E2, LS1

  • E2-24: UMBRA AND PENUMBRA - COLOR FILTERS

    E2-24
    Identify the source of penumbra regions.
    Combined red and green filters project nearly white light on a screen. When the foam sphere is inserted between the sources and the screen, the penumbral regions take on the color of the filter through which the light in that region has traveled, because the other color has been blocked by the disc. The umbra, where light from both sources is blocked, is nearly black.
    E2, LS1

    e2-24a

  • E2-42: TELESCOPE MODEL

    E2-42
    Show how a telescope can view any point in the sky using a universal mount.
    Using this type of mount, which provides two independent rotations, the laser can be adjusted to aim at any point in the lecture hall. If the laser were a telescope, it would therefore be able to look at any point in the sky using this mechanism.
    E2

  • H2-11: SOUND LENS

    H2-11
    Demonstrate focusing of sound by refraction in a sound lens
    A balloon filled with carbon dioxide acts as a focusing sound lens, due to its convex shape and the smaller velocity of sound in the carbon dioxide. When the lens is inserted between the loudspeaker and the microphone, the sound wave is focused, increasing the sound level at the microphone, as seen on the oscilloscope. The source is either a small chunk of dry ice in a flask or a cylinder of carbon dioxide.

    For comparison, air (very little focusing) and helium (defocusing) balloons can also be provided upon request.

    For good results, position the microphone and the loudspeaker about 40 cm apart, inflate the balloon to about 20 cm diameter, and use a frequency of about 2-4 kilohertz.

    If you use additional balloons of different gases, as mentioned above, have students make predictions about what effect density will have before showing the result.
    H2, OM1, ME2. ME3, I0, FS1

  • L1-01: ARC LAMP - PROJECTION OF ARC

    L1-01
    Direct projection of side view of the arc of a carbon arc lamp.

    A 10cm focal length lens is used to project a side view of the arc of a carbon arc lamp onto a screen. The shield protects the class from the direct light of the arc.

    Remember that due to the inversion of the image by the lens, the image of the arc is upside down!

    geol1-01a

  • L1-02: TUNGSTEN-HALOGEN LAMP - PROJECTION OF LAMP

    L1-02
    View an operating tungsten-halogen lamp.
    A 20cm focal length lens is used to project the image of a tungsten-halogen lamp from one of our bright point sources onto a screen.

    Be aware that this image can be very bright, and the components can become hot; use caution, and do not leave on for an extended period.
    LS1, OM1

    l1-02a

  • L1-04: POINT SOURCE - FLASHLIGHT BULB

    L1-04
    Demonstrate optical characteristics of a "point source"
    Light from the point source propagates in straight lines from the source outward. It can be seen at the same place by everyone, and casts a shadow in every direction, etc.

  • L1-11: INVERSE SQUARE LAW - LIGHT BULB AND RADIOMETER

    L1-11
    Demonstrate that light obeys the inverse square law.
    The intensity of the bulb as a function of distance can be measured by a radiometer, verifying the inverse square relationship. The radiometer reading is displayed using an overhead projector slave meter.
    OS0, ME2, OM1

    l1-11a

  • L1-12: INVERSE SQUARE LAW - OVERHEAD PROJECTOR AND TWO-METER STICK

    L1-12
    Show that light obeys the inverse square law.
    With the lens one meter from the screen the area lit by the projector beam is measured. Moving the lens back to two meters from the screen, the width and height of the lit area both double, so the area is four times as great and the intensity is one-fourth for twice the distance. This demonstrates that the inverse square law has as much to do with geometry as with wave propagation.
    OS0

    l1-12a

  • L1-21: PINHOLE IMAGE - GROUND GLASS SCREEN

    L1-21
    View individually a pinhole "image."
    A pinhole in the back end of the outer box (left front) casts an "image" on a ground glass screen at the enclosed end of the inner box (front of box at right rear). The image is viewed through the open end of the box (at the rear) as the inner box is slid back and forth to change the size of the image

  • L1-22: OPTICAL BOARD - PINHOLE CAMERA

    L1-22
    Demonstrate how a pinhole "image" is formed.
    The camera is represented by the region between the two baffles on the optical board. The left baffle has a small slit representing the pinhole, and the right baffle has a light surface to make the ray visible. Hold the carousel projector by hand and shine it at the "camera." from a position at the left of the optical board. The position of the source and the position of the "image" are related.

  • L1-23: PINHOLE VIDEO CAMERA

    L1-23
    Produce video images with a pinhole camera.
    The lens has been removed from a video camera and pinholes of 0.020 inches and 0.032 inches can be threaded onto the camera's lens mount as seen at left above. The experimental setup for producing the images shown below is seen in th erighthand photo. The images formed these two pinholes are shown at left and center below. At right is the image produced by a standard 45-mm fixed focus lens for comparison.
    L1, AV

    l1-23

    l1-23bl1-23cl1-23d

  • L1-24: PINHOLE TV CAMERA

    L1-24
    Demonstrate a pinhole "image" using a TV camera.
    A pinhole of either 0.032 inch or 0.020 inch is positioned on the front of a TV camera, replacing the lens. The resulting image on the videcon of the TV camera is a "pinhole image." Change pinholes to vary the resolution of the image. It can be used with other objects as long as they are well lighted.
    L1, OF4

    l1-24a

    l1-24bl1-24cl1-24d

  • L1-33: LASER BEAM EXPANDERS

    L1-33
    Expand a laser beam to uniform 10mm or 40mm diameter.
    Screw-on laser beam expanders are available for use with the laser on the laser cart shown in the photograph. Beams produced are 1cm diameter and 4cm diameter.

    l1-33al1-33b

  • L2-01 OPTICAL BOARD - PLANE MIRROR

    L2-01
    Demonstrates reflection from a plane mirror

    This demonstration shows that the angle of incidence is equal to the angle of reflection. A bright white light source is directed through a baffle with several slits, producing a set of rays. Lenses are used to collimate these rays, and they are then reflected off of a long plane mirror. If the lenses are adjusted such that the incoming rays are approximately parallel, the reflected rays will be as well.
    Engagement Suggestion
    Optionally, you can use slits with colorful filters to show that this is good for all colors. Challenge students to predict what will happen if you switch to the color filters – will different colors reflect at different angles? Why or why not?
    Background
    Unlike light diffracted through a lens or prism, reflected light from a surface is unaffected by the frequency of the light. The reflection off of a flat mirror is dependent only on the angle the light strikes at. Thus, there should be no chromatic aberration in a reflecting telescope, one reason they are valuable for astronomical use.
    FS1

  • L2-02: OPTICAL BOARD - RAY DIAGRAM - PLANE MIRROR

    L2-02
    Demonstrate how several light rays are used to locate the image in a plane mirror.
    A single central ray passes through a half-silvered mirror, with half deflected to act as the source at the tip of an object. By rotating the top mirror it can be shown that all rays starting at the object point (the rotating mirror) appear to come from the corresponding point behind the plane mirror (the image point). The image is a faint arrow at the right of the photographs.
    FS0

    l2-02a