Light and the Properties of Reflection & Refraction OBJECTIVE To study the imaging properties of a plane mirror. To prove the law of reflection from the previous imaging study. To study the refraction of light through glass. To prove the law of refraction from the previous study. INTRODUCTION A ray of light is a line representative of the direction of travel of radiant energy. In general, a line is used to represent a single beam of light. A ray of light will, typically, travel in a straight line until it encounters some object. The material encountered determines what the ray does next. The reflection of light occurs when an incident ray strikes the surface of a material and a reflected ray comes from the surface. If the object is optically transparent, the incident ray will not only reflect, but refract. Refraction is the deviation of the incident ray toward or away from the normal to the surface, as it passes into the material. Various parameters including the material encountered, the incident ray's angle to the normal, the reflected ray's angle to the normal, and the refracted ray's angle to the normal are used to derive the relations known as the Laws of Reflection and Refraction. A single plane mirror and a glass plate will be used to prove these laws. APPARATUS One mounting board, one plane mirror with holder, one thick square glass plate, one metric ruler, one laser pointer with line attachment, a protractor, six colored pencils, and four long straight pins (ONE colored & THREE white). Light and the Properties of Reflection & Refraction - Page 1
THEORY When light is emitted from a source, it is radiated outward in all directions in a straight line. Depending on the test performed on the light, the light may act as a particle or a wave. The study of reflection and refraction use the principles of the wave behavior of light. The location of a subsequent position on each wave designates a wave front. Ray Wave Front Wave of Light Figure 1 Source A ray is used to represent the direction of propagation of the wave front as it travels outward from the source. Note that the ray is perpendicular to the wave front. Additionally, the wave fronts are approximated as being parallel to each other in what is termed the "far field approximation." Reflection: When a ray strikes a surface, typically, some of the light is reflected from the surface of the object. The rays, upon striking the surface, obey the "Law of Reflection": θ i = θ r Equation 1 The law states that, the angle of incidence (the angle between the incident ray and the normal to the surface) is equal to the angle of reflection (the angle between the reflected ray and the normal to the surface). The normal (a line perpendicular to the surface) is drawn at the point where the incident ray strikes the surface. Figure 2 Light and the Properties of Reflection & Refraction - Page 2
The surface type determines how the reflected ray will behave as it leaves the surface. The surface types are either perfectly smooth or rough. A smooth surface is defined as one where multiple reflected rays move off parallel to each other. A rough surface is defined as one where multiple reflected rays do not move off parallel to each other. The Law of Reflection still holds for both surfaces. The each of the normal lines for the smooth surface are always parallel to each other, whereas, the normal lines at the rough surface vary their direction across the surface. These surface types are illustrated below. Figure 3 Smooth Surface Rough Surface Reflection from a smooth surface is called regular, or specular, reflection and reflection from a rough surface is called irregular, or diffuse, reflection. When objects are imaged by a reflecting surface, like a mirror, it is required that a minimum of two rays, emanating from the object, be used to locate the image of the object in the reflecting surface. The intersection of these two rays locates the image. If the rays actually intersect to form the image, we say that the image is real. However, if the light rays do not actually intersect, but must be extrapolated in order to intersect, we say that the image is virtual. Plane mirrors produce virtual images. One of the two rays, used to locate an object's image, is drawn perpendicular to the surface while the second ray is drawn at any other angle other than perpendicular. Figure 4 illustrates this process. Figure 4 Where, do and di are the distances from the object to the mirror=s surface and the distance from the surface to the image, respectively. For a plane mirror, the object distance equals the image distance (do = di). Light and the Properties of Reflection & Refraction - Page 3
Refraction: When a ray strikes an optically transparent surface, part of the incident ray will be reflected at the surface and part of the incident ray will be refracted into the material. Refraction occurs as a bending of the incident ray as it passes into the material. This bending occurs due to the difference in velocity of the light between the two media (the one it came from and the one it is passing into). The transmission or bending occurs at the same point where the incident ray and the normal intersect. Figure 5 The relation between the incident angle, the refracted angle, and the two media is referred to as the "Law of Refraction" or "Snell's Law": n 1 sin θ i = n 2 Equation 2 c n= v Equation 3 sin θ r Where, n1 [#] and n2 [#] are called indices of refraction. They are material constants that indicate the relative speed of light in that material (medium): Where, the index of refraction n [#] is given as the ratio of the speed of light in a vacuum c [m/s] to the speed of light passing through some material v [m/s]. When v = c, the index of refraction is equal to one (the index of refraction of a vacuum and approximately air). When an incident ray moves from a medium where the index of refraction is lower than the index of refraction of the medium to which the ray enters (n1 < n2), the refracted ray will bend toward the normal. Similarly, the refracted ray will bend away from the normal when n1 > n2. ' Light and the Properties of Reflection & Refraction - Page 4
EXPERIMENTAL PROCEDURE Due to the nature of the procedures and the information learned by DOING each activity, ALL experiments are to be done individually. Reflection: The Rule of Reflection: a) Lay a vertically-oriented sheet of paper flat on the table (not on the mounting board) and draw a horizontal line 4 cm from the top edge of the sheet. Near the middle of this line, draw a normal that extends at least 10cm from the line. Figure 6 Using a mirror holder, stand a mirror on its edge along the horizontal line so that the reflecting side of the mirror points towards the normal and the center of the mirror is approximately lined up with the normal. Use the laser pointer with its line attachment projector to place a beam of light along your sheet of paper towards the mirror. Aim the beam so it reaches the mirror at an angle other than 90 o. The beam should intersect the mirror at the location where you drew the normal. Using a colored pencil, mark the path of the beam both toward and away from the mirror. b) Using a different colored pencil than in part a, move the laser line so that the beam strikes the mirror at a different angle at the normal and repeat part a. c) Clearly label each item and location on both mirror plots; this should include (but not limited to) the incident beam, the reflected beam, the mirror, the angles, etc. d) Measure and record on your diagram the angle between the incident beam and the normal. e) Measure and record on your diagram the angle between the reflected beam and the normal. Reflection: Imaging Properties of a Plane Mirror: Single Object: Light and the Properties of Reflection & Refraction - Page 5
a) Lay a new vertically-oriented sheet of paper flat on the table (not on the mounting board) and draw a horizontal line near the middle of the sheet. Figure 7 Place this sheet on your mounting board and arrange the plane mirror and holder along the line on the sheet. b) Stick a COLORED pin (object) near the right side of the mirror approximately 6 cm perpendicular to and in front of its surface. Mark its location as the object pin. c) A second WHITE pin (reference pin #1) is to be placed several centimeters to the left of the object pin. Mark its location with a colored pencil. d) A third WHITE pin (reference pin #2) will be placed such that its location is in the same straight line as reference pin #1 and the image of the object pin (behind the mirror). You will need to be at eye-level with the surface of the board. In addition, closing one eye will aid in the proper alignment of the pins. Line up only the bottom part of the pins during this procedure...not the head's of the pins!!! Mark its location with the same colored pencil you used in "c". This scenario is illustrated below: Mirror Reference Pin #1 Figure 8 Reference Pin #2 Colored Object Pin Light and the Properties of Reflection & Refraction - Page 6
e) Using a different colored pencil than you used to mark your first set of pins, repeat parts (c) and (d) leaving the object pin alone but for a different starting locations for reference pin #1 (closer to the mirror, farther from the mirror, more to the left, more to the right, etc.). f) Using a different colored pencil than you have previously used, repeat parts (c) and (d), one final time, again leaving the object pin alone but for a different starting location for reference pin #1 (closer to the mirror, farther from the mirror, more to the left, more to the right, etc.). At this point you should have THREE pin pair sets (each set a different color). g) Clearly label each item and location point on your mirror plot; this should include (but not limited to) the object pin, the reference pins, etc. h) Connect the first two locations marked as reference pin #1 and #2 with a line of the same color used to mark their locations. The line connecting these two points should be extended up to the mirror's surface. i) Repeat this procedure for the other two sets of reference pin locations. j) Extrapolate each drawn line backwards, with a dashed line of the corresponding color, to the area behind the mirror s surface; the line should extend to the edge of your paper. Figure 8 is an illustration of this result. k) Indicate the location of the image. Triangle: a) Lay a new vertically-oriented sheet of paper flat on the table (not on the mounting board) and draw a horizontal line near the middle of the sheet. Figure 9 Light and the Properties of Reflection & Refraction - Page 7
b) Draw the figure illustrated below 6 cm in front of the line as shown. B A Figure 10 C AB is approximately 5 cm long and 6 cm from the mirror and BC is approximately 3 cm long. c) Place this sheet on your mounting board and arrange the plane mirror and holder along the line on the sheet. d) Place a COLORED object pin at point A and locate the image of this pin (object) based on the previous procedure (c, d, & e...not f). You will have TWO pin pair sets (each set a different color) for point A; each pair in a different color. e) Repeat for the object pin placed at point B. f) Repeat for the object pin placed at point C. g) Clearly label each location point on your mirror plot; this should include (but not limited to) the object pins, the reference pins, etc. h) Connect the first pair of like-color reference pin A locations together with a line of the same color used to mark the locations. The line connecting these two points should be extended up to the mirror's surface. Repeat for the other set of like-color reference pin A locations. i) Repeat this procedure for the reference pin locations for B & C. j) Extrapolate each drawn line backwards, with a dashed line of the corresponding color, to the area behind the mirror s surface; the line should extend to the edge of your paper. You will have a total of six differently colored lines; two each for pins A, B, & C. k) Indicate the location of the image of each of the points A, B, & C. Once you have located each of these points, connect each of the image points together as if the entire object were reconstructed in the mirror. Light and the Properties of Reflection & Refraction - Page 8
Refraction: a) Lay a new vertically-oriented sheet of paper flat on the table (not on the mounting board) and lay the thick square of glass flat down near the center of the sheet and trace around its perimeter. The two brushed surfaces of the plate should be facing the right and left sides of the paper while the transparent surfaces should be facing the top and bottom sides of the paper. Pick the glass plate up, move it out of the way, and 1 cm from the right edge, along the top of the plate, draw a normal to the outline of the plate. Be sure to extend this normal line from the top to the bottom of the page, through the plate, and out its opposite side; as illustrated in Figure 11. Figure 11 b) Now, place this sheet on the mounting board, replace the glass plate in its proper location, and stick a pin at the intersection of the normal and the top edge of the plate; this will be referred to as the normal pin. c) Place a pin approximately 6 cm vertically upward from the top edge of the plate and 2 cm to the right of the normal line; this will be referred to as the reference pin [Reference Pin A]. d) Look through the bottom edge of the glass plate (NOT above the top of the block but through its body!!) and place a pin (sighting pin #1) along the bottom edge of the plate (right up against the glass) such that this pin, the normal pin, and the reference pin all appear to be in the same straight line. Light and the Properties of Reflection & Refraction - Page 9
e) Place a final pin (sighting pin #2) such that this pin, sighting pin #1, the normal pin, and the reference pin all appear to be in the same straight line. Be sure to mark each of these pin locations prior to removing them from the board. Figure 12 illustrates this setup. Normal Line Reference Pin Normal Pin Glass Plate Figure 12 Sighting Pin #1 Sighting Pin #2 f) On the same paper, in a different color, repeat d & e for the reference pin placed approximately 6 cm from the top edge of the plate and 4 cm to the right of the normal line [Reference Pin B]. g) Finally, on the same paper, in a different color, repeat d & e for the reference pin placed approximately 6 cm from the top edge of the plate and 6 cm to the right of the normal line [Reference Pin C]. h) Clearly label each location point on your mirror plot; this should include (but not limited to) the object pins, the reference pins, etc. i) Removing all the pins and the glass plate, draw a straight line from each reference pin location to the normal pin location using the corresponding color that was used to mark their locations. j) Continue by drawing a correctly colored straight line from the normal pin location to the location of each of the respective sighting pin #1 locations; sighting pin A goes to reference pin A, etc. k) Conclude by drawing a correctly colored straight line from the location of sighting pin #1 to sighting pin #2. Light and the Properties of Reflection & Refraction - Page 10
l) Measure and record the angle between the normal line of each of the reference pin locations on the diagram and in the data table; these are your incident angles. m) Measure and record the angle between the normal line of each of the sighting pin #1 locations on the diagram and in the data table; these are your refracted angles. n) Draw a NEW set of normal lines at the glass block's surface where each of the sighting pin #1s touch the block. o) Measure and record the angle between this new normal line of each of the sighting pin #2 locations on the diagram and in the data table; these are your exit angles. COVER PAGE REPORT ITEMS (To be submitted and stapled in the order indicated below) (-5 points if this is not done properly) Completed Laboratory Responsibility and Cover Sheet DATA (worth up to 60 points) Each of the four labeled diagrams constructed in the procedure. Additionally, a data table for Refraction is available as a downloadable Excel file DATA ANALYSIS (worth up to 30 points) For the Rule of Reflection Activity Summarize your observations in the first mirror exercise (using the laser line) as a rule describing how to predict the path of a beam of light that is aimed at a mirror. This will become your "Rule for Reflection." Is your rule true for all angles or only for certain angles? Light and the Properties of Reflection & Refraction - Page 11
For the Imaging Properties of a Plane Mirror (Single & Triangle) Activity From your data, deduce a general set of rules governing the imaging properties of a plane mirror. Consider the following questions in order to gain insight for your final set of rules: What is significant about the location where the three constructed lines cross over each other in the single object plot? What can you conclude as to the minimum number of lines of sight necessary to locate the image of an object in a plane mirror? What can you conclude about the location of the object, in front of the mirror, compared to the location of the image, behind the mirror? For the Refraction Activity From your data, deduce the rules governing the refraction of light through a glass plate. o How do the three angles within this figure (incident beam angle, refracted beam angle, and exit beam angle...all measured from their respective normal lines) compare to each other? Should there be a relationship between them? If so, what is it and if not, explain why not. o An additional required sample calculation for the refraction activity, to be shown on the bottom of the accompanying data table, is highlighted in yellow on the downloadable Excel data table spreadsheet GRAPHS (worth up to 0 points) None GRAPH ANALYSIS (worth up to 0 points) None CONCLUSION (worth up to 0 points) None QUESTIONS (worth up to 0 points) None Light and the Properties of Reflection & Refraction - Page 12