A Galilean telescope is formed by a long positive focal length objective lens and a short negative focal length eyepiece, so it produces an erect image. The lens at the left is used to produce parallel rays of light, as if from a distant star. The parallel beam of rays entering the objective lens is wider than that emerging from the eyepiece, indicating the ability of the telescope to "gather" light. When the position of the "star" is changed by moving the source up, the image is moved up and the angle at which it is viewed is magnified relative to the incoming light, indicating the ability of the telescope to produce angular separation of the stars it is viewing.

Choice of slit baffle and distance of baffle from source determine the number of rays and their spacing.

Magnification is obtained by using a magnifying glass that has a focal length much shorter than the near point of the eye. The magnification M=f(eye)/f(lens), where f(eye) is the near point of the eye. The object to be viewed is located at the focal point of the magnifying glass, which is held close to the eye.

The eyepiece on most optical instruments, such as telescopes, microscopes and binoculars is a magnifying glass.

The TV camera functions as the eye, so what the eye sees can be viewed on a monitor or the rear projection screen. A 5 cm convex lens acts as the objective lens, producing a real, inverted and magnified image of the source about 5 cm from the eyepiece, which is adjacent to the camera lens. The eyepiece acts as a magnifying glass, magnifying the real image created by the objective lens. The camera lens is focused at infinity, modeling a relaxed eye. Magnification is achieved by making the image distance for the objective lens greater than the object distance. Shown below are the video camera "eye" views of the meter stick directly (left) and through the "microscope."

To set up in practice, set the camera focus and lens positions and move the object until the image is seen by the camera.

The TV camera functions as the eye, so what the eye sees can be viewed on a monitor or the rear projection screen. At the left below is a direct view of the object scale by the video camera as displayed on the monitor. A 10 cm or a 5 cm convex lens acts as the eyepiece and a 20 cm convex lens is the objective lens for the telescope, with the TV camera focused at infinity (relaxed eye). The rule is positioned across the lecture hall (at infinity) from the telescope. The image is seen to be inverted and to have a magnification M=f(ob)/f(eye). The magnification can be checked by viewing a two-meter stick with the TV camera directly (left) and then with the telescope. The image with a 10 cm eyepiece has a magnification of 20/10=2, seen in the center picture. The image with a 5 cm eyepiece has a magnification of 20/5=4, seen in the picture at the right.

To set up in practice, set the camera focus and lens positions and move the objective lens until the image is seen by the camera.

The TV camera functions as the eye, so what the eye sees can be viewed on a monitor or the rear projection screen. A 10 cm or 5 cm convex lens acts as the eyepiece, a large 20 cm convex lens is the objective lens, and a 10 cm convex inverting lens between the objective and the eyepiece, with the TV camera focused at infinity (relaxed eye). The rule is positioned across the lecture hall (at infinity) from the telescope. The image is seen to be erect and to have a magnification M=f(ob)/f(eye). The magnification can be checked by viewing a two-meter stick with the TV camera directly and then with the telescope.

The photographs below show the image with no telescope (left), using a 20cm focal length eypiece (M=2), and using a 10cm focal length eyepiece (M=4). Vignetting is seen in both telescopic images, and is very obvious in the center image.

To set up in practice, set the camera focus and lens positions and move the objective lens until the image is seen by the camera. The inverting lens is used with equal object and image distances (twice the focal length), and provides no magnification.

The TV camera functions as the eye, so what the eye sees can be viewed on a monitor or the rear projection screen. A 10 cm or a 5 cm concave lens acts as the eyepiece and a large 20 cm convex lens is the objective lens, with the TV camera focused at infinity (relaxed eye). In this case the image of the objective lens is on the left side of the concave eyepiece - behind the eyepiece. The rule is positioned across the lecture hall (at infinity) from the telescope. The image is seen to be erect and to have a magnification M=f(ob)/f(eye). The magnification can be checked by viewing a two-meter stick with the TV camera directly and then with the telescope. Compared with the astronomical telescope, the image is more faint and has a smaller high-quality field of view.

The images below show the object rule viewed directly by the camera "eye," the telescope image with a 10cm fl eyepiece (M=2) and the telescope image with a 5cm fl eyepiece (M=4).

To set up in practice, set the camera focus and lens positions and move the objective lens until the image is seen by the camera.

The object consists of an illuminated transparency containing a field of o's and x's. Light from the object is focused symmetrically by a 10 cm converging lens to an intermediate focus, which in turn is focused onto a distant screen by a 20 cm convex lens. A second 10 cm convex lens, the field lens, can be rotated into the beam at the position of the intermediate image. With the field lens out, the image is clear and bright near the center but very dim near the periphery of the image, a phenomenon known as vignetting. When the field lens is inserted, light illuminating the entire image is kept within a small enough angle that it passes through the lens system. Vignetting is virtually eliminated, and the image is uniformly well lighted. The photographs below show the final image with and without the field lens, at the same scale for direct comparison.

Many types of projectors use field lenses to obtain the greatest illumination for the projection bulb used.

The field lens, heat absorber, and lamp with built-in reflector can be seen, and their functions discussed.

The picture at the center shows the projector turned upside down with the open access port to view the optical elements. The photograph at the right shows, in some detail, the bulb (right center), the mirror (bottom near center) directing the light beam toward the lens (upper left, not seen), the heat filter (left center) and the field lens (just above the heat filter). Note that the bulb has a built-in reflector that directs the light beam onto the mirror, and the field lens focuses the beam so that after passing through the slide (just above the field lens, under the cover) the entire beam passes through the slide projector zoom lens to give the brightest picture.

A lens has a focal length twice that of a convex mirror. The lens is positioned at a distance of twice the focal length of the mirror (the focal length of the lens) in front of the mirror. An object is placed a distance of twice the focal length of the lens in front of the lens. The image position, at the same point as the object position, can be determined by calculation and verified by this demonstration. The photograph below shows the real, inverted image on the baffle.

A convex mirror and a concave lens with the same focal length are positioned one focal length apart and the object post is positioned one focal length in front of the lens. The location of the image, behind the mirror, can be calculated and then verified experimentally using this demonstration. The picture at the top right views down along the optic axis of the setup to show the optical elements as they are aligned.

The image is located at the position of the rod at the right end of the optical rail above (behind the mirror). This can be verified by parallax viewing between the image and the rod at that position, as seen in the photographs above. The three pictures directly above show the parallax alignment of the image with the alignment post, as seen from along the optic axis and from each side. In the center picture you can see the unfocused object wire as a blur in front of the lens. Note that you want to align the image post with the image seen in the mirror directly - not the image as seen through the lens, which can be seen near the bottom in the pictures.