BRIGHTNESS CHANGES WITH DISTANCE 49 



squares about 6 cm. on a side. You can do this by heating the 

 bottom of the candle with a burning match until a little of the 

 wax has melted and dropped upon the middle of the cardboard. 

 Then press the candle against the cardboard until the wax has 

 hardened. 



In a room that is dark, light the larger candle, and place near 

 it some opaque, upright object, such as two spools of thread 

 one on top of the other. Have both the candle and the spools 

 on a piece of white paper. Examine the shadow behind the 

 spools, and see that it has two parts, one (the umbra) much 

 darker than the other (the penumbra). Draw a sketch of the 

 shadow, labeling each part, but not shading it. 



b. Carry out the same test with the small candle; then try 

 a larger source of light,' such as a kerosene or electric lamp. 

 The lamp must be reasonably near the spools. Draw the 

 shape and size of the umbra and penumbra in each case, and 

 compare them. 



c. Now put the two candles as close together as possible, and 

 place the spools near them. 



Note how the shadows, and their parts, cross one another. 

 Draw these parts, labeling them. Then slowly move the 

 candles apart, noting the effect upon the umbra and penumbra. 

 What is the effect of a large flame, or of separate flames, upon 

 the size of the penumbra? 



EXERCISE 48 

 BRIGHTNESS CHANGES WITH DISTANCE 



Apparatus and Materials. Cardboard square 4 cm. on a side, sheet 

 of paper, metric rule, checkerboard, " birthday "' candle. 



a. Out of cardboard cut a square piece 4 cm. on a side; then 

 draw on a piece of white paper a large square divided into 16 



