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Geometrical Optics

  • L6-05: OPTICAL BOARD - RAY DIAGRAM - VIRTUAL IMAGE POS LENS

    L6-05
    Use principal rays to locate a virtual image produced by a convex lens.
    The central ray passing through a half-silvered mirror serves as the optic axis, and the vertical ray between the two mirrors serves as the object arrow. By rotating the mirror at the tip of the arrow the three principal rays (or other rays) can be produced, all of which appear to be emanating from the image point. The focal points of the lens, about 17" (43cm) from the lens surface, can be indicated using squares of masking tape or black tape. A single converging lens in front of the object is used to keep the ray narrow. The object should be about 30cm from the surface of the lens. The image position is found by tracing the principal rays back behind the object with a meterstick or by rotating the object mirror while watching where the rays cross.

    l6-05a

  • L6-06: MULTIPLE PINHOLES AND LENS RECOMBINATION

    L6-06
    Demonstrate that a lens focuses light.
    The black housing at the left in the picture contains a clear bulb with a W-shaped filament, which can be focused on a distant screen at the right. With the lens rotated out of the light from the source, several pinholes are poked into a sheet of tin foil covering one end of the aluminum tube in the center of the photograph, producing several pinhole "images" on the screen. When the lens is rotated back into the light, all of the images from the pinholes are combined into a single true image. The image of the pinholes is compared with the image of the lens in the photographs below. Click on one of the photographs below to see an mpeg video of the transition from pinhole "images" into a single image.
    L6, OM1

    l6-06a

    l6-06b

    l6-06c

  • L6-07: MICROWAVES - LENS

    L6-07
    Demonstrate that a paraffin lens can focus microwaves.
    When the 12cm microwave transmitter and receiver are placed about 50 cm apart the receiver picks up the microwaves and displays them on an overhead projector meter. Positioning the lens at an appropriate point between the transmitter and the receiver focuses microwaves onto the receiver, increasing the meter reading. The geometry can be optimized by moving the receiver along the optic axis.
  • L6-08: REAL IMAGE OF CONVERGING LENS - LIGHT BULB

    L6-08
    Show the real image of a converging lens.
    An incandescent bulb with printing on the top is used as an object to be imaged with lenses of different focal lengths. Hold the lens above the light bulb at a distance slightly greater than the focal length of the lens to cast an image of the trademark onto the ceiling. Change lenses to change the magnification. (10cm and 20cm focal length lenses tend to work best in most rooms, but 5cm, 30cm, and possibly others can also be available upon request.)
    OM1, LS1
  • L6-09: REAL IMAGE OF CONVERGING LENS

    L6-09
    Show the systematics of real image formation by a converging lens.

    An arrow/disc object baffle lit from behind by a bright point source of light is used as the object, and various convex lenses are used to cast images of the key onto a screen. The effect of variation in focal length and object distance can be readily seen. Lenses with 10cm, 20cm, and 30cm focal length are provided.

    Combinations of two convex lenses or a concave and a convex lens used together can also be demonstrated. Please request additional lenses if desired.

  • L6-10: IMAGE LOCATION WITH TV CAMERA - LENS

    L6-10
    Locate both real and virtual images of a convex lens
    The lens on the lecture table forms either a real or a virtual image of the digits on the ruler in the holder at left. The TV camera is then focused on that image. Moving the scale to the side of the optic axis, the image location will be the position at which the scale is in focus. This technique can be used to locate either a real or a virtual image.
    OM1, OS0, OF4
  • L6-11: OPTICAL BOARD - DEPTH OF FIELD

    L6-11
    Illustrate the idea of depth of field of a (camera) lens, and to locate the near and far points.
    The beams passing through lenses 1 and 2 are focussed to produce an object for lens 3, the "camera" lens, which is imaged on a distant screen at the right as a straight line. Adjust the screen position so that the image is as sharp as possible, and mark the object point on the optical board with black tape. By moving lens 2, the position of the object is changed, eventually causing the image to become blurred. Mark the near and far points on the board for an acceptably clear image line. The result as obtained here is somewhat arbitrary, but in fact there is a mathematical definition for what constitutes a sharp image.
  • L6-12 MAGNIFYING LENS IN WATER

    L6-12
    Shows that focal properties of a lens depend on the medium in which the lens is located
    A small fuse box is mounted on a holder at a distance less than the focal length behind a convex lens, so the lens acts as a magnifying glass. Note, in the photo at the left, the magnification of the fuse box when the system is in air. Then dip the entire lens-object system into water. Because there is much less bending of the light at the water-glass interfaces than at the air-glass interfaces, the magnification is much less
    L6, L4

    geo

  • L6-13: OPTICAL BOARD - PARALLEL RAY FOCUS

    L6-13
    Demonstrate focusing of parallel rays in a counterintuitive way.

    Parallel rays entering from the left in the photograph at the left above are focussed to a point by a plexiglass double convex lens. At the right above the same rays are shown displaced upward by rotation of a rectangular plexiglass block, but without the focusing lens.

    Q: What will happen to the transverse (vertical) position of the focal point when the rectangular block is rotated while the lens remains at the same point? Will the focal point be displaced upward, be displaced downward, or remain at the same lateral position? A: The focus will remain at the same point, as seen in the photographs below. In fact, all rays parallel to those shown in the photograph will focus at the same point, in the absence of aberrations. This is a fundamental property of how lenses act to focus light.

    The parallel rays are formed by a second double convex lens out of the photograph to the left.

    l6-13a

    l6-13b

  • L6-14: IMAGE OF CONVEX LENS - WITH AND WITHOUT BAFFLE

    L6-14
    Encourage thought regarding how an image is formed.
    An arrow/circle cross object is imaged on a screen by a 150mm focal length convex lens, as seen in the center photograph above. The experimental setup is shown below, with the object at the left, the lens in the center, and the image screen at the right in the photograph. A paper baffle is then stuck onto the lens, as seen in the photographs below, blocking half of the light passing through the lens. What happens to the image? Encourage your students to make a prediction. Will it remain unchanged; will it become brighter; will it become fainter; will the left side be gone, or will the right side be gone? Shown also are the image without the baffle on the focusing lens and with the baffle on the focusing lens. The image with the baffle in place is clearly fainter than the original image, as can be seen.
    OM1, OM2, LS2, office

    l6-14a

    l6-14b

    l6-14c

  • L6-21: OPTICAL BOARD - DIVERGING SPHERICAL LENS

    L6-21
    Determine the focal point of a concave lens.
    Parallel rays incident on a diverging plano-concave spherical lens appear to emanate from the focal point of the lens. Optionally, two plano-concave diverging lenses can be placed together to increase the divergence and decrease the focal length. A slit baffle with concave and convex lenses may be used to create a set of parallel rays, which can be varied in number, color, and in spacing.

    geo

  • L6-22: OPTICAL BOARD - RAY DIAGRAM - VIRTUAL IMAGE NEG LENS

    L6-22
    Use the three principal rays to locate the virtual image of a diverging lens.
    The central ray passing through the half-silvered mirror serves as the optic axis. The vertical ray between the two mirrors serves as the object arrow. By rotating the mirror at the tip of the arrow, the three principal rays (or any desired ray) can be produced. The tip of the image is located at the point from which the three principal rays appear to diverge, which can be determined using a meter stick and marking the point with black tape. The focal length of the lens is about -34". Two lenses may be hung back-to-back to shorten the focal length to about -17", which increases the divergence and may aid in viewing ease but at the expense of image size. The single convex lens before the object helps to keep the light ray narrow. Do not use the extreme edges of the lens to avoid serious spherical aberration.

    l6-22a

  • L6-31: STRING MODEL - SPHERICAL ABERRATION

    L6-31
    Illustrate light rays for spherical aberration.
    Rays emanating from a single point object but with different divergence are illustrated as they go through a spherical lens. Those rays further from the optic axis are focused closer to the lens, because the spherical lens has too much curvature at larger angles. The model shows proportional displacements but is not to scale, and aberrations are exaggerated.

    l6-31a

  • L6-32: OPTICAL BOARD - SPHERICAL ABERRATION IN LENS

    L6-32
    Demonstrate spherical aberration using rays.
    Rays from a point source are focused by a convex spherical lens. If the entire lens is used, considerable spherical aberration results. Reducing the aperture (equivalent to reducing the f-number of a lens) by sliding the slit baffle away from the source reduces the spherical aberration. Alternatively, spherical aberration can be eliminated entirely by using an aspherically corrected lens, such as the hyperbolic lens shown at the right.

    l6-32a

  • L6-33: STRING MODEL - CHROMATIC ABERRATION

    L6-33
    Ilustrate rays for chromatic aberration.
    Rays emanating from a single point with the same divergence but with different colors (red, yellow, and blue) are illustrated as they pass through a spherical lens. Blue rays are focused closer to the lens than red rays. The scale of the model is exaggerated for clarity of observation.

    l6-33a

  • L6-34: OPTICAL BOARD - CHROMATIC ABERRATION IN LENS

    L6-34
    Show chromatic aberration in a convex lens.
    Choose appropriate baffle for a central ray with two extreme rays. The chromatic aberration, seen as dispersion in either of the two extreme rays, can be enhanced by cutting off part of the outgoing dispersed ray with a card or your finger. A closeup of the focal point at the right above shows the chromatic aberration.

    l6-34a

  • L6-35: CHROMATIC ABERRATION - POINT SOURCE AND 20 CM LENS

    L6-35
    Show the effect of chromatic aberration in a lens.

    Two 20cm convex lenses are available: a simple spherical lens and an achromat. Light from the point source is focused onto a slit by a cylindrical lens placed immediately in front of the source, which in turn is imaged by the 20-cm spherical lens onto a distant screen, as shown in the photograph at the left above. The screen is then rotated as shown at the right above to increase the dispersion at the image.

    The image of the achromat, shown at the right below has virtually no chromatic aberration compared with that of the ordinary simple lens, seen at the left.

    l6-35a

    l6-35b

    l6-35c

  • L6-36: STRING MODEL - ASTIGMATISM

    L6-36
    Illustrate rays for on-axis astigmatism.
    Rays from a single point source with a single divergence are focused by a lens which has a cylindrical component of curvature. Here the focal length of the vertical focus is shorter than the focal length of the horizontal focus, as seen in the pictures at the left above. The upper picture, taken from the horizontal plane including the central ray, shows the vertical focus. The picture at the right above, taken from an angle above the horizontal, shows the waist between the horizontal and vertical foci.

    l6-36a

    l6-36b

  • L6-37: ASTIGMATISM

    L6-37
    Demonstrate off-axis astigmatism with a spherical lens.
    A bright point source is focused onto a small circular aperture which acts as the source. The 50cm focal length convex lens then focuses this spot onto a distant screen. If the lens is rotated about 30 degrees it will produce off-axis astigmatism, which can be seen as follows: Keep the screen perpendicular to the optic axis while moving it along the optic axis to see (moving outward from the astigmatic lens from left to right in the photographs below) (1) the beam immediately following the lens, (2) the horizontal focus (a vertical line), (3) the waist, (4) the vertical focus (a horizontal line), and (5) the expanding beam following the second focal point.

    l6-37al6-37bl6-37c

    l6-37dl6-37e

  • L6-38: COMA

    L6-38
    Illustrate coma.
    The filament of a bright point source (about 3x6 mm) is focused onto a distant screen using a 20 cm focal length convex spherical lens, producing the image at the right in the center photograph above for paraxial rays. A plane front-surface mirror is used to direct a bundle of non-paraxial rays through the lens, producing the image at the left in the center photograph, which displays coma. The large baffle before the large 20cm lens and the iris following the lens limit stray light so that the two images are clearly differentiated.

    l6-38a

    l6-38b