L-3: Optical Instruments

OBJECTIVE:

To construct a number of optical instruments and measure magnification.

APPARATUS:

Identical to the of L-2 plus white board, achromatic doublets, Ramsden eyepiece.

SUGGESTION: In constructing an optical instrument catch the real image formed by the first lens on paper. This location can tell where the next lens goes; e.g. for a telescope or microscope place the next lens slightly less than its focal length beyond the first image.

EXPERIMENTS:

1. Inverting Telescope

   A.

   First measure the $f$ of a weak converging lens ( $25 \leq f \leq 50$ cm) and of a strong converging lens ($f \sim 5$ cm). The first lens ($f$ large) typically has the virtue of intercepting and focusing a fairly large area of light while the second lens can be positioned to give a large virtural image (and hence magnification.) Notice that if the first image, $q_1$is at a point $p_2 > f_2$ with respect to the second lens you get a real, erect second image. If you are using the web-based lab manual and desire a demonstration, click on the Inverting Telescope Demo button immediately below.

   Use you will use these two lenses to construct an astronomical (inverting) telescope. As an object, use the white board and scale while illuminated by a bright light. As a procedure for measuring the magnification, vary the space between the objective L$_1$ and the eyepiece L$_2$ until the virtual image $I_2$ of scale S seen through L$_2$ lies in the plane of S (i.e. $p_1+d=\vert q_2\vert$). As a sensitive test of this there should be no parallax between the scale as seen directly by your eye 2 and the scale image seen by eye 1 thru the telescope as shown in Fig. 2. Generally a person will adjust the eyepiece so that the virtual image appears at the distance of most distinct vision ($\sim$25 cm).

   Figure 1: The inverting telescope (not drawn to scale).

   

   Figure 2: View scale with one eye, then the other.

   

   B.

   Adjust the telescope direction until these images superimpose (as in Fig. 3). The number of divisions on the scale as viewed directly (by eye 2) which fall in one division of the image as seen through the telescope (by eye 1) is clearly the magnifying power of the telescope. Compare your measured magnification $M$ with that calculated for an astronomical telescope, namely $M= f_1/f_2$ where $f_1$ is the focal length of the objective and $f_2$ that of the eye piece. Why are the two different? Calculate the magnification from the actual measured object and image distances. Compare with the measured $M$.

   Figure 3:

2. Erecting telescope

   Figure 4: Configuration of a three lens erecting telescope.

   

   A.

   Measure the focal length, $f$, of a second strong converging lens and use it as the inverting lens L$_3$ (Fig. 4) to form an erecting telescope. L$_2$ must be adjusted to give a real image, I$_2$. Notice that varying the space between I$_1$ and the inverting lens L$_3$ changes the magnification. If you are using the web-based lab manual and desire a demonstration, click on the Erecting Telescope Demo button immediately below. In this simulation your are now able to readjust both the positions and focal lengths!

   B.

   What position of the inverting lens makes the shortest possible telescope, (i.e. it makes the distance between I$_1$ and I$_2$ a minimum)?

3. Simple microscope or magnifier: Experiment with one of the strong converging lenses as a magnifier until you can make the virtual image appear at any distance you choose: vary the object distance from zero to the focal length. The parallax test described in Part 1 will enable you to locate the virtual image. When the parallax between the object and the virtual image (seen through the lens) vanishes, the object and virtual image are in the same plane.

4. Compound microscope: Use the two strong converging lenses to form a compound microscope.

   Figure 5: Setup for compound microscope.

5. Galilean telescope (or opera glass): Make use of the weak converging lens and a strong diverging lens.

OPTIONAL:

1. Ramsden eyepiece

   A.

   Ask the instructor for the holder containing a Ramsden eyepiece, a crosshair, a diaphragm, and an objective lens. See Fig. 6.

   Figure 6: Construction of a Ramsden eyepiece.

   

   The Ramsden eyepiece consists of lenses 1 and 2, plano-convex lenses of $f= 85$ mm. Spherical aberration is less than for a single lens because the ray bending is spread over four surfaces. It is a minimum if the curved surfaces face one another as shown. (In addition if the two lenses were their focal length apart, chromatic aberration would be a minimum. But, since dirt specks on lens 1 then would be in focus, lenses 1 and 2 are usually set $2f/3$ apart). The tube also contains an objective lens to convert the tube into a telescope or microscope.

   B.

   Use the Ramsden eyepiece with $d=2f/3$ in the telescope and microscope. Note improvement in image over that of a single eyepiece lens. Adjust eyepiece for a sharp image of the cross hairs. Then move the objective lens until the image shows no parallax with respect to the cross hairs.

2. Huygens eyepiece: A common eyepiece in which the image (and hence cross hair) is within the eyepiece. It also employs two plano-convex lenses but both convex surfaces are toward the incident light. Minimum lateral chromatic aberration exists for a separation of ($f_1+f_2)/2$. Usually $f_1 \sim 3f_2$.

   Figure 7: Construction of a Huygens eyepiece.

   

3. Eye ring.

   A.

   Point the astronomical telescope at a lamp and explore with a screen the illumination back of the eyepiece. [Or remove diaphragm from telescope or microscope of optional (1)].

   Figure 8: Position of eye ring.

   

   The light coming through the telescope has a minimum cross section at ER. This area ER is the image of the objective formed by the eyepiece. Obviously all light which gets through the telescope must go through this image, and thus ER is the best spot to place the pupil of the eye. Hence the name ``eye ring''.

   Note that if one places a diaphragm with aperture appropriately larger than the eye ring a little ahead of the eye ring, then an observer looking through the aperture would position the pupil of her/his eye on the eye ring.

   B.

   Using the Ramsden eyepiece, place the diaphragm at the appropriate distance in front of the eye ring. Note the improvement in the ease of observing through it, especially for the compound microscope.

4. OPTIONAL telescope: Use an achromatic objective lens, of long focal length and a commercial Ramsden eyepiece (from instructor). Note the quality of the image.
5. OPTIONAL microscope: Use a short focal length achromatic objective and a commercial Ramsden eyepiece (from instructor). Note the quality of the image.

   It is interesting that one does not need an achromatic eyepiece because the virtual images for red and blue, though at different distances (e.g., red at 2 m, blue at $\sim \infty$), subtend almost the same angle at eye. As a result the eye doesn't notice the aberration.