powered lamps makes it very difficult to tell when the two sides of the screen are equally illuminated. Longer photometer bars should be used for comparing the stronger lamps. Since a carbon filament lamp does not give the same candle-power, when observed from different directions, the socket should always be turned so that the lamp appears broadside on to the screen.

Place the standard lamp in the socket at one end of the photometer, and connect a voltmeter across the terminals of the lamp. The lamp is then connected up in series with the source of current and a rheostat. This rheostat is to be adjusted until the voltmeter reading is that marked on the lamp. The unknown lamp is to be connected up in the same way, except that an ammeter should be in series with the rheostat.

When the voltage across both lamps is the same, adjust the screen so that both sides appear equally bright, or until the spot in the center comes nearest to disappearing as seen from both sides. Then record the distances r, and r2. Make three settings. Now change the rheostat so that the voltage at the unknown lamp is lowered about two volts and get the candle-power and other readings as before. Repeat in steps of two volts until the unknown lamp has a voltage of 90.

Plot a curve with candle-powers as ordinates and voltages as abscissæ. Calculate the watts per candle-power consumed by the unknown lamp for each voltage and plot a second curve with watts per candle-power as ordinates and volts as abscissæ.

Repeat the experiment using another lamp of different type. Plot these curves on the same diagrams as were used for the first lamp.

What conclusions can you draw as to the relative efficiencies of the lamps?

EXPERIMENT NO. 502

THE PLANE MIRROR.

References: Stewart, Physics, Sect. 568-574; Kimball, College Physics, Sect. 818-821; Duff, College Physics, Sect. 416418, 421; Spinney, Text-Book of Physics, Sect. 478-480.

The purpose of this experiment is to test the law of reflection of light and the law for the location of the image of an object in a plane mirror.

(a) Fasten a large sheet of paper to a drawing board. Using a sharp pencil, draw a straight line, AB, across one end of the sheet and about two inches from the edge. At a point, C, on AB, erect very carefully a perpendicular, CD, and draw another line, CE, making an angle of more than 20° with the perpendicular. Be very careful to make this line go exactly through the point C. Set a plane mirror perpendicular to the paper with its REFLECTING surface directly over the line AB. Put two pins, 1 and 2, carefully on the line CE, several centimeters apart and perpendicular to the paper. From a position on the other side of the perpendicular, look at the images of these pins in the mirror so that the images appear in a line, one behind the other. Put a pin, 3, near the mirror in the same straight line as these images and another, 4, farther from the mirror on the same line of sight. Remove the mirror and draw a line through the points 3 and 4. This line should pass through the point C; call it CF. Line EC represents an incident ray of light and CF the same ray after reflection. Measure with a protractor angle ECD, the angle of incidence, and angle DCF, the angle of reflection, and record the values under suitable headings. Repeat the procedure five times, drawing other perpendiculars along AB. The law of reflection applies to any beam of light, but it is not wise to use angles of incidence of less than 20° in this experiment because of the relatively large percentage of error inevitable in measuring small angles with a common protractor.

(b) Draw a straight line, AB, across the sheet near the middle, so there will be 10 to 15 centimeters of paper available on each side of the line. Set the plane mirror with its REFLECTING surface on this line and draw an arrow several centimeters in front of the mirror and roughly parallel to it. Call the arrow PP'. Set a pin carefully at P. Now set a pin, E, several centimeters to the right of P and another, F, to the left of P. Look over pin E at the image of P in the mirror and set a pin so as to mark this line of sight. Do the same with pin F. The image of P lies at the intersection of these lines of sight. Before moving the mirror, repeat the procedure and find the two lines. which locate the image of P'. Then remove the mirror, draw the lines and locate both images. Connect the two image points.

Draw a straight line from P to its image. What angle does this line make with the reflecting surface? Measure and record the distances of P and its image from the mirror. State the laws of image location illustrated here.

Mirrors of polished metal or of black glass are preferable to the common silver-backed mirrors, because in the former types the reflection takes place at the front surface. What would be the effect on your results of using a thick mirror, the back surface of which was the reflector?

EXPERIMENT NO. 503

THE CONCAVE MIRROR.

References: Stewart, Physics, Sect. 575-583; Kimball, College Physics, Sect. 823-829; Duff, College Physics, Sect. 422425; Spinney, Text-Book of Physics, Sect. 481-483, 485.

In this experiment, the purpose is to measure the focal length and radius of curvature of a concave, spherical mirror and to test the law of the size of the image.

(a) Throw the image of a distant object (a building for example) upon a screen held in front of the mirror. The rays of light from the object to the mirror may be considered parallel, thus the distance from the screen to the middle of the mirror is the principal focal length. Determine the focal length from five separate trials, each time using a different object, and calculate the average result.

(b) If an object is placed at a distance, p, from the mirror, and its image falls at a distance, q, from the mirror, then p and q are called conjugate focal lengths. Calling F the principal focal length, we have the relation :

Determine p and q by the method of parallax as follows: Clamp the mirror in a vertical position and place a pin on the stand in front of the mirror at a distance of about one and three-quarters times the focal length, as found in (a). Now

mount a second pin on a stand and place it farther from the mirror than the first. Look at the image of the first pin in the mirror and move the second pin to such a position that the point of the second pin appears to be in contact with the image of the first pin, and will remain in contact when you move your head from side to side. Be sure and pay no attention to the image of the second pin. If there is difficulty in making the adjustment remember that whichever is nearer to the eye, the pin or its image, will appear to move the faster as you move your head sidewise.

The distances from the two pins to the mirror, when adjustment is complete, are conjugate focal distances, p and q. Calculate F. Repeat with three slightly different positions of the first pin.

(c) Now use only one pin and make it coincide with its own image as in part (b). Measure the distance from the pin to the mirror. This pin is now at the center of curvature of the mirror. Repeat three times. What is the relation between the distance found in this case—that is, the radius of curvature— and the principal focal length found in parts (a) and (b)?

(d) Proceed as in (b), but use two short paper scales instead of pins. Locate the image of the first scale, using the second scale as an indicator. The second scale should face the observer, the first scale, the mirror. The image of the first scale should be exactly superimposed on the second scale, and there should be no parallax. Determine how many divisions on the object correspond to a given number on the image. From this observation calculate the magnification. According to the theory however, the magnification should be equal to the ratio of the respective distances of the two scales from the mirror. Test this law for three different positions.

EXPERIMENT NO. 504

THE INDEX OF REFRACTION OF GLASS.

References: Stewart, Physics, Sect. 588-592; Kimball, College Physics, Sect. 837-838; Duff, College Physics, Sect. 431432; Spinney, Text-Book of Physics, Sect. 486, 508. One definition of the index of refraction of a substance states that the index is the ratio of the sine of an angle of in

cidence to the sine of the corresponding angle of refraction. By tracing the path of a ray of light from air through a square block of glass, we can determine a pair of these angles and find the index of refraction of the glass relative to air.

Place the glass block flat upon a sheet of paper so that the transparent edge coincides with a straight line which has previously been drawn across the paper. (The paper should be placed upon a drawing board.) Stick one pin vertically in the paper against the back edge of the glass block, and a second pin near the middle and against the front of the block.

Now place your eye in such a position that when looking through, not over, the glass block the two pins seem to coincide. Put a third pin about six inches in front of the block so that it seems to coincide with the other two. Draw a line perpendicular to the face of the block where the second pin was placed. Draw a line through the first and second pins, and also through the second and third. These lines are the path of a ray of light in the air and in the glass, and the angles which these lines make with the perpendicular, as drawn above, are the angles of incidence and refraction, respectively. Measure these angles with a protractor and from a trigonometric table find the values of the sines of the angles and calculate the index of refraction, which is given by the formula:

sin i

n

sin r

Repeat for four different positions of the pin behind the glass block, tabulate the data, and enter at the foot of your table the mean value of the refractive index for the sample of glass used in this experiment.

A square glass cell filled with liquid may be used in place. of the glass block and the index determined for the liquid.