telescope and the astronomical telescope and to study the images formed.

Four lenses are supplied, three converging lenses of different focal lengths and one diverging lens. Find the approximate focal lengths of the converging lenses by focusing on a card the image of some distant object and measuring the distance from the lens to the image in each case.

(a) The compound microscope. Mount on the optical bench at one end a metric scale and at a distance somewhat more than its focal length set the converging lens of shortest focal length. This is the objective lens. Place another converging lens of short focal length on the optical bench to serve as the eyepiece. Look through it and move it about till an image of the scale is clearly seen. By looking through the microscope with one eye and past it with the other, both eyes being open at the same time, try to determine the magnification by estimating how many centimeters of the scale are covered by one centimeter of the image. Describe the images formed by the two lenses, as to nature, size, and position.

(b) The Galilean telescope. Use the long-focus converging lens as the objective and the diverging lens as the eyepiece. Look through the instrument at a large wooden scale across the room and test its magnification by the method described in (a). Look at some distant object through the open window. Describe the images formed by both lenses in this instrument.

(c) The astronomical telescope has an objective lens of long focal length and a converging eyepiece of short focal length. Set a pair of such lenses on the optical bench and point the instrument out the window. Hold a screen back of the objective lens and focus on it an image of some distant object. Is the image real or virtual, larger or smaller than the object, erect or inverted? Place a cardboard diaphragm, having a circular aperture provided with a cross-thread, at the same position as the screen and move the eyepiece until, on looking through it at the aperture, both the cross-thread and image are clearly seen. Get rid of parallax as far as possible. Describe the image.

(d) The magnification produced by an astronomical telescope is very nearly the ratio of the focal length of the objective to that of the eyepiece, if the object is viewed from a great

distance. At shorter distances, this ratio does not hold. Point the telescope at the large wooden scale and find the magnification produced at distances of 4, 7, 10 and 15 meters and at as great a distance as is possible in the laboratory. Take the apparatus into the corridor if necessary. In each case record the object distance and the magnification. At the larger distances it is essential that the scale be well illuminated. In which case does the magnification approach most closely the ratio of the focal lengths? What is the effect on magnification of bringing the object nearer? Is there such a thing as a fixed magnifying power for a telescope?

If the instructor so directs, plot a curve using magnifications as ordinates and object distances as abscissae.

EXPERIMENT NO. 509

THE SPECTROMETER.

References: Stewart, Physics, Sect. 629, 596; Kimball, College Physics, Sect. 896-899, 851; Duff, College Physics, Sect.

495, 433; Spinney, Text-Book of Physics, Sect. 508, 509, 512-515, 486.

The methods described in Experiments 504, 505, and 506 give us only the mean value of the refractive index for light of all wave-lengths. On the other hand, the very fact that a prism forms a spectrum shows that the index is different for light of different wave-lengths. Consequently, to determine the index with a high degree of accuracy, it is necessary to use light of a definite wave-length, and it is most convenient to have the substance in the form of a prism.

It is shown in many text-books of physics that the angle of deviation by a prism depends upon the angle at which the light enters, but that this angle has a minimum value when the light enters and leaves at the same angle. Moreover, it is shown that if D is the value of this angle of minimum deviation and A is the angle of the prism, the index is given by the formula:

n

sin (A+D)

sin A

The angles, A and D, can be measured very accurately with a spectrometer. The prism is mounted on the table of the spectrometer and is adjusted so that its edge is parallel to the axis of the table. The optical axes of the telescope and the collimator are also to be perpendicular to the axis of the table. These adjustments are already made when the apparatus is supplied to the student and he should be careful not to disturb prism or adjusting screws, or the adjustments will be thrown out.

To measure A, the angle of the prism, turn the prism-table till the angle to be measured points directly toward the collimator, and clamp it in this position. Place a fish-tail gas burner, an ordinary oil lamp or a candle in front of the slit. The light coming from the collimator is split by the angle of the prism and reflected to both sides. Consequently, the telescope can be placed in such a position that it receives the light reflected from the right face of the angle and forms an image of the slit in the plane of the cross-wires. The slit must be made. so narrow that its image is only a line of light and the telescope is then moved till this image coincides with the vertical crosswire. Then both verniers are read. Now move the telescope to the other side, again get the image on the cross-wire, and read again. The difference between the readings on the two sides gives twice the angle A. (The student is to prove that this is true.) Make three trials for A.

To find the angle of minimum deviation, D, turn the prism so that the light from the collimator passes through it, forming a spectrum, and place the telescope so that this spectrum appears in the focal plane of the eyepiece. Now replace the fishtail burner by a sodium burner. The spectrum then formed will consist of a single bright yellow line, because the light emitted by a sodium-flame is all of the same wave-length (practically), whereas the fish-tail burner emits waves of all lengths and therefore gives a continuous spectrum.

Now if the prism-table be rotated, this yellow line will move up to a certain position and then move back, so that it is impossible to get it past this point. This is the position of minimum deviation. Set it in this position, place the cross-wire on it, and read both verniers.

To get the other reading for the angle, D, we could remove the prism and set the telescope so that it receives directly the light from the collimator. However, it is easier to turn the prism, so that the spectrum is formed on the other side and locate the position of minimum deviation on that side. The prism-table must be loosened from the graduated circle while this shift is being made and while the prism is being set in the new position for minimum deviation. Failure to loosen it will result in destroying the value of the first setting and in making necessary a complete new trial. After finding the settings for minimum deviation on both sides of the prism, we obtain D by taking half the difference between the two settings.

After making two trials for D with sodium light, make two trials with the light from lithium. It is possible to arrange a burner to give a steady, constant light with lithium as with sodium, but a brighter light is secured, for a few seconds at a time, if the lithium chloride solution be fed into the flame on an iron wire. One observer should feed it in, while the other makes the settings for minimum deviation. The solution may be fed right into the sodium flame, so that the red lithium line and the yellow sodium line both appear at the same time, but in different places.

Finally, calculate the index for sodium light and that for lithium light, to the third decimal place.

Caution: This method is very accurate if moderate care is taken. Be sure to have the slit very narrow. Do not strike the telescope with the hand or the head; move it from place to place by taking hold of the brass arm that carries it.

EXPERIMENT NO. 510

DIFFRACTION AND INTERFERENCE.

References: Stewart, Physics, Sect. 647, 651-658; Kimball, College Physics, Sect. 924-926, 928, 932-935; Duff, College Physics, Sect. 455-458, 464-465; Spinney, Text-Book of Physics, Sect. 516, 518, 519.

The phenomena of interference and diffraction are fundamental in the study of light, for it was through the evidence.

gained from experiments along these lines that the wave theory of light overthrew the corpuscular theory previously in favor. The following experiment illustrates a few of the phenomena of diffraction and interference.

(a) With a sharp knife cut a slit across the center of a piece of thin cardboard, without cutting through at the edges. Place a screen containing a very small circular opening in front of a fish-tail burner or lamp flame. Stand several feet from the lamp and view the illuminated aperture through the slit, holding the cardboard close to the eye. Make a sketch of the appearance of the circular hole.

(b) While viewing the aperture, rotate the slit about the line of sight as an axis. Does the image rotate with the slit? Is the light spread out parallel to the length of the slit or perpendicular to it?

(c) Look through the slit and change the slit width by pulling the edges of the card. Describe the effect on the image. of widening the slit.

(d) Repeat these three tests, substituting a long, narrow slit for the small circular opening near the lamp. Make sketches illustrating the appearance of the image when the two slits are parallel and when they are perpendicular to each other.

(e) Replace the fish-tail burner with a sodium burner. The former gives out light containing all wave-lengths in the visible range, while the latter gives out light of essentially a single wave-length. Repeat part (d) with this monochromatic light and note any difference between the images now obtained and those obtained with white light.

(f) View the bright slit in front of the sodium flame successively through the three pairs of parallel slits ruled in the film of a photographic plate. These three pairs of lines are differently spaced. Describe carefully the results obtained. Are the bright and dark bands spread out most when the slits are far apart or close together?

(g) Examine the image formed by looking through a part of the plate where a number of parallel lines have been ruled to form a coarse diffraction grating. Describe carefully what

you see.