428 



NATURE 



{March 28, 1878 



one edge of the square is brightly lighted by the sunbeam, 

 and if the mirror is placed at an angle of forty-five degrees 

 with the sunbeam, the other edge of the square is lighted 

 up by the second beam. 



In Fig. I, A is the beam of light from the heliostat, 

 and B is the beam reflected from the mirror, that is marked 

 M. To make this more simple, we call the first beam the 

 beam of incidence, and we say that it travels in the direc- 

 tion of incidence, as shown by the arrow. The second 

 beam, marked A, we call the beam of reflection, and the 

 course it takes we call the direction of reflection. The 

 point marked O, where the light strikes the mirror, is 

 called the point of incidence. 



In the diagram is a dotted line representing a quarter 

 of a circle reaching from the beam of incidence to the 

 beam of reflection. A quarter of a circle, as you know, 

 is divided into ninety degrees. Another dotted line 

 extends from o at the mirror to x on the quarter-circle, 

 and divides it into two parts. Half of ninety is forty-five, 

 and hence the mirror stands at an angle of forty-five 

 degrees with both beams of light. Now the line A and 

 the dotted line reaching from o to x make the angle of 

 incidence, and the angle between B and the line from o to 

 X is the angle of reflection ; and the curious part of this 

 matter is, that these two angles are always equal. Here 

 they are both angles of forty- five degrees. 



Move the mirror about in any direction, and measure 

 the angles of incidence and the angles of reflection, and 

 these angles will always be exactly equal. 



If you look at the diagram you will see that the mirror 

 is at an angle of 45 degrees with the beam of incidence, 

 and that the beam of reflection is at an angle of ninety 



Fig. 2. 



degrees with the incident beam. Hence, if the mirror is 

 tilted through a certain angle, the reflected beam is tilted 

 through twice this angle. For instance, if the mirror is 

 moved i degree, the beam of reflection moves 2 degrees. 

 Place the mirror at an angle of 22^ with the beam of 

 incidence, and the beam of reflection is at angle of 45. 

 Move the mirror to an angle of 67^, and the beam of 

 reflection will move round to an angle of 135 degrees. 



Fig. 2 represents the two postal-cards fitted on 

 blocks of wood that we used in a former experiment, 

 and the three blocks of wood we cut out at that time. 

 The five blocks are placed close together in a line, and 

 with the postal-cards at the ends. A lighted lamp is 

 placed near one of the cards, and on the middle block is 

 a small piece of window-glass that has been painted with 

 black varnish. A single coat of black varnish on one 

 side of the glass is all that is required to give us the 

 black mirror needed in this experiment. Place the lamp 

 close to the card in such a position that the flame will 

 be just on a level with the hole in the card. If the lamp 

 is not convenient the blocks and cards may be placed 

 upon a table facing a north window in full daylight. 



When everything is ready look through in the postal- 

 card marked B, down upon the black mirror, and on it 



you will see a single spot of light, the reflection from the 

 lamplight or the light from the window shining through 

 the hole marked a in the drawing. Get the needle- 

 pointed awl and place it so that the point will just touch 

 the spot of light in the black mirror, and then fasten the 

 awl in this position with a piece of wax, as represented in 

 the picture. 



You will readily see that this experiment is the same 

 as the last. Again we have a beam of light reflected 

 from a mirror. The beam of incidence passes through 

 the postal-card at A and finds its point of incidence on 

 the mirror, and the beam of reflection extends from 

 the point of incidence to the second card at B. 



Take a sheet of stiff paper 10 inches (25*4 centimetres) 

 long, and about 4 inches (10 centimetres) wide, and hold 

 it upright between the two cards, with the bottom resting 

 on the mirror. With a pencil make a mark on the edge 

 of this at the point of incidence marked by the awl, and 

 at the hole in the card where the beam of incidence 

 enters, and marked A in the drawing. Draw a line 

 between these two points and you have an angle formed 

 by this line and the base of the paper. This angle marks 

 the angle of incidence. Put the paper on the blocks with 

 the ruled line toward the card B, and you will find that 

 the line fits here equally well. It now extends from the 

 point of incidence to B, and proves that this angle is the 

 same as the other, that both sides are alike, and that the 

 angle of incidence and the angle of reflection are equal. 



Take out the block in the middle and move the others 

 nearer together till they touch. Repeat the experiment : 

 make a measurement with a piece of paper as before, and 

 draw a line on it from the point of incidence to either of 

 the holes on the cards, and then compare the angles thus 

 found, and in each case they will be exactly alike. Take 

 out another block and try it again, and you will reach 

 the same result. 



These experiments show us that there is a fixed law in 

 this matter, and the more we study it the more we are 

 convinced that it has no exceptions. 



Experiment in Multiple Reflection 



Choose a south room on a sunny day and close the 

 blinds and shutters at all the windows save one, and at 

 this window draw down the curtain until only a narrow 

 space is left at the bottom. Close this space with a strip 

 of thick wrapping-paper, and then cover the rest of the 

 window with a blanket or shawl so as to make the room 

 perfectly dark. Then cut a round hole the size of a five- 

 cent piece in this paper, and through this hole a slender 

 beam of sunlight will fall into the darkened room. 



Bring a hand-mirror into this beam of light and the 

 beam of reflection will make a round spot of sunlight on 

 the wall above the window. This spot of light is a pic- 

 ture 01 the sun thrown by the mirror upon the wall. 

 Hold the mirror at an oblique angle in the sunbeam and 

 direct the beam of reflection upon the opposite wall. 

 Now there are several reflections, brilliant spots of light. 

 If the spots of light do not stand out sharp and clear, 

 turn the mirror slowly round and you will soon find a 

 position for the glass that will give six or more reflections. 



How does it happen that a common looking-glass can 

 thus split a single sunbeam into several beams ? If you 

 touch a pencil to a mirror you will notice that while the 

 point of the pencil touches the glass the point of the 

 reflected pencil seen in the mirror does not meet the point 

 of the real pencil, and that there is a little space between 

 them. The reflection we see in the glass is from the 

 smooth surface of the quicksilver at the back of the glass, 

 and the space between the reflection and the pencil is 

 filled by the glass. 



Hold a sheet of common window- glass before a lighted 

 lamp or candle, and you will see a faint reflection of the 

 flame in the glass, and at the same time you can readily 

 see through the glass. This shows us that the outside 



