Properties of Light

PROPERTIES OF LIGHT

Part 1: Reflection

OBJECTIVE: To study and verify the law of REFLECTION using plane mirrors. [Note: The results of this experiment will depend on the accuracy and neatness of your work. A sharp pencil is required since a dull point may throw off an angle by as much as five degrees.]

TERMINOLOGY: reflection object image virtual image normal

THEORY: The Law of Reflection states that if the incoming light forms i r an angle of incidence (i) with a line normal to the surface, then the light reflected off the surface will form an angle of reflection (r) with the normal line which is equal to the angle of incidence. This is shown in Figure 1. Fig. 1

PROCEDURE: 1. We will determine the path of light rays by sighting along two or more pins stuck through paper into the soft board. By connecting the holes left in the paper by the pins with a straight line, the paths of the light rays can be recorded. The angles and distances can then be measured with protractor and ruler. On a piece of paper draw a line to represent the reflecting surface of the mirror Then about 5 cm apart, draw two lines normal (perpendicular) to the first line. Place the paper on the soft board. Place the mirror on the paper with the back of the mirror on the line for the reflecting surface and the scratch on the mirror on the right hand normal.

2. Push a pin into the paper at a point about 2 cm to the left of the left-hand normal and about 5 cm from the mirror. This pin (#1) will be your object, and the location of its IMAGE will be determined by the following procedure.

3. With your eye level with the surface of the paper, determine the reflected ray by lining up a second pin with the image of the first pin and the scratch on the mirror. When you have them lined up, push the second pin into the paper.

4. Without removing the pins, slide the mirror over so that the scratch is now on the second normal. Determine a second reflected ray in the same manner as you did the first.

5. In order to locate the position of the image on your paper, place the paper on a smooth surface. Draw lines from the location of the first pin to intersections of the normals and reflecting surface. These lines represent your INCIDENT rays. Next draw a line from the location of the second pin to the intersection of the righ thand normal and reflecting surface. This is one REFLECTED ray. Draw the second ray in a similar manner. Extend the lines representing the reflected rays behind the reflecting surface until they intersect. The point of Properties of Light 2 intersection is the location of the image.

6. Measure and label the angles of incidence and reflection. Theoretically they are equal. Measure and label the image and object distances from the reflecting surface. Theoretically they are also equal.

REPORT: 1. For each of the two incident rays, is the angle of incidence equal to the angle of reflection as theory states? 2. What kind of image is formed by a plane mirror. a real or virtual image? (A real image can be seen on a piece of paper if the paper is placed at the location of the image. A virtual image cannot be seen on a piece of paper. It only appears to our eyes that light comes from this image.) 3. Is the object distance equal to the image distance as theory predicts? 4. What could cause any discrepancy between your results and the theoretical predictions?

Part 2: Refraction from a plane surface

OBJECTIVE: To study and verify the law of REFRACTION (Snell's Law) using a a glass block.

TERMINOLOGY: refraction index of refraction

THEORY: n1 Snell’s Law states that if the incoming light is traveling in a medium with an index of refraction of n1 and forms an angle of 1 with a line n2 normal to the surface as shown in Figure 2, then the light that enters the second medium of index n will form an angle of with 2 2 2 the normal line where the refracted angle is given by the equation Fig. 2 n1 sin1 = n2 sin2 (1)

Snell’s Law predicts that the light will get bent (refracted) toward the perpendicular line if n1 < n2 (such as for light in air entering glass) and will get bent away from the perpendicular line if n1 > n2 (such as for light in glass entering air).

PROCEDURE: 1. Place a fresh piece of paper on the soft board. Lay the glass block down on the paper. Place one pin (#1) right next to an unfrosted side near the middle of that side. This pin will be our object. Since it is touching the glass plate, we can assume that it is actually just inside the glass plate (like a coin at the bottom of a swimming pool is just inside the pool).

2. Now view this pin from the other side. Position your eye so that the image of the pin seen through the glass is aligned with the pin as seen above the glass. Place another pin (#2) on this line as close to the glass plate as possible. The line formed by the original pin (the object) and this pin should form a line perpendicular to surface of the glass plate, and the distance between these two pins should be the actual distance that the object pin is inside Properties of Light 3 the glass.

3. Now place a pin (#3) 1 cm to one side of the second pin and against the glass plate. Again place another pin (#4) 1 cm to the side of pin #3 and against the glass plate. And finally, place another pin (#5) 1 cm to the side of pin #4 and against the glass plate. Now align your eye with pin #3 and the image of the object pin (#1) in the glass, and place a pin along that line (pin #6). Do the same for pin #4 (with pin #7), and for pin #5 (with pin #8).

4. Now remove the glass plate from the board, and draw a line connecting pins #8 and #5 and extend it to the area where the glass plate was. Do this for pins #7 and #4, and for pins #6 and #3. Finally do it for pins #2 and #1. All lines should cross at approximately one location which would be the image position of the object pin (#1) inside the glass plate.

5. Measure the real distance that pin #1 is inside the glass plate, and measure the apparent distance (the distance that pin #1 appears to be inside the glass plate). From Snell's law and geometry, the following formula can be derived as long as angles are small:

dapparent = dreal / n (2) where n is the index of refraction of the glass. From this expression, calculate the index of refraction of the glass.

REPORT: 1. What type of image (real or virtual) is seen through the glass? 2. Where does the image appear to be? 3. What is the index of refraction of the glass? 4. Does water do the same to light that glass does? Justify your answer Properties of Light 4

Part 3: Thin Lenses

OBJECTIVE: To study and verify some of the laws of optics applicable to thin lenses by determining the focal length of a lens by two methods and by determining the magnification of a lens by two ways.

TERMINOLOGY: focal length object distance image distance real image magnification

THEORY: Each point of a self-luminous object or reflection object (O) is a source of light with a large number of rays emanating from it in all directions. A lens will alter the direction of those rays which strike it, and an image (I) of the object may be formed. If rays from a single point on the object strike different parts of the lens and eventually all intersect at some other point in space, a real image is formed. Real image formation is illustrated in Figure 3. A virtual image is formed if the projections of the rays from a single point on the object intersect at a single point in space. A screen placed at this point will not reveal an image, but the image is visible to the brain if observed from the proper position such that the diverging rays enter the eye. See Figure 4.

s s’

h F I O h’ f

Fig. 3. Real Image Formation

s’ s’ s s

h’ F h h h’ I O O F I

f f (a) with converging lens (b) with diverging lens

Fig. 4. Virtual Image Formation

A thin lens is one whose thickness is negligible in comparison to the image and object distances Properties of Light 5 [object distance is measured from object to lens; image distance is measured from lens to image position]. There are two kinds of lenses. A convex lens is thicker in the center than at the edges. Such a lens is also called a positive lens or a converging lens. A concave lens is thinner at the center than at the edges. It is also called a negative lens or a diverging lens.

The axis of a lens is the line drawn through the centers of curvature of its refracting surfaces. If a beam of rays parallel to the axis is incident on a converging lens, the beam is brought to a focus at a point on the axis called the focal point (F). If a beam of rays parallel to the axis is incident on a diverging lens, the rays diverge as though radiated from a point on the axis. This point is also called the focal point (F). The distance along the axis from the focal point to the center of the lens is known as the focal length (f). A converging lens has a positive focal length; a diverging lens has a negative focal length.

There are at least three commonly used symbols for object and image distances:

object distance: s (used here) , o (sometimes used) , p (sometimes used) image distance: s' (used here) , i (sometimes used) , q (sometimes used)

These distances and the focal length are related by the “thin lens equation”,

1/s + 1/s' = 1/f . (3)

Object distances, image distances, and focal lengths can be positive or negative. In this experiment, all will be positive.

The ratio of the image size (h’) to the object size (h) can be predicted by use of the lateral magnification factor Mexp = h’ / h . (4)

[NOTE: If the image is inverted relative to the object, then h’ is negative, making M negative.]

As seen in Fig. 3, geometry gives a theoretical lateral magnification in terms of the object and image distances: Mthe = -s' / s . (5)

[NOTE: The minus sign in Eq. (3) is necessary to keep the signs of the experimental and theoretical magnifications consistent. That is, when s’ is positive, h’ is negative.]

Two methods will be used to measure the focal length of a convex lens:

1. Parallel rays. If the object is sufficiently far away so that s»f, the rays will be parallel, and the object will be focused at the focal point of the lens (f = s'). This method is used in Step1.

2. The thin lens equation. The image and object distances (s' and s) will be measured and f calculated with Eq. (3) . This method is used in Step 2.

PROCEDURE: 1) Place only the convex lens and the white screen on the optical bench and aim the lens at Properties of Light 6 some object outside the room. (If possible, perform this part of the experiment in the hallway with the hallway lights off and with the lights in a far room on.) Move the lens or screen along the bench until the image is focused as sharply as possible. Measure and record the image distance, which in this case is assumed to be the same as the focal length.

2) Place the slide on the optical bench. By shining a light through the slide, we will use the lens to form an image of the slide on the screen. Hence the slide will become our object in this part. Next place the lens at some position beyond the focal length from the object and focus an image of the object on the screen by moving the screen.

a) Measure object and image distances and calculate the focal length. b) The length of one of the object arrows is h = 30 mm. Measure the length of an image arrow, h’. (If you cannot image the entire arrow clearly, then use the large or small circle as your image and measure the diameter of this image circle. This diameter is the value of h’. The object circles have diameters of 20 mm and 10 mm. Use the appropriate value for h.) The ratio of h’ to h gives an experimental value of the magnification by Eq. (4). The theoretical value of the magnification depends on s and s' as expressed in Eq. (5). Calculate the magnification using each expression. Do the two ways of finding magnification give the same result if experimental uncertainty is considered? Is the image upside-down or right-side-up? c) Repeat the measurements and calculations in (a) and (b) above for two more object distances. d) Average the three resulting focal length values. e) Are the three values of Mexp the same? Should they be?

REPORT: Perform all of the calculations and answer all of the questions in the Procedure. Properties of Light 7

Part 4: The Telescope

OBJECTIVE: To see how a refracting telescope works and to investigate what we mean by the resolution of an imaging system.

TERMINOLOGY: refractor reflector magnifying power visual acuity radians resolving ability objective lens eyepiece

THEORY: There is a limit to what the eye can "resolve", that is, there is a limit to the smallest detail that the eye can see. This limit of visual acuity can best be described in terms of an angle () formed as in Figure 5(a) below. To calculate this angle we can use the definition of angle in radians:

(radians) = arc length / radius

If the angle is small, as it will be in this experiment, then the height of the object is approximately the arc length and the distance to the object is approximately the radius. Thus, as shown in Fig. 5(b), we can say that:

(radians) = height of object / distance to object (6)

radius  distance to object arc length height of  object

(a) (b) Fig. 5. Angles

We can convert angles in radians to angles in degrees by noting that there are 360 in one circle and there are 2 (where  = 3.14...) radians in one circle. Hence we can convert radians into degrees by:

(degrees) = (radians) x 360/2 (7)

(For small angles, each degree can be divided up into 60 arc minutes and each arc minute can be further divided up into 60 arc seconds.)

A telescope can help us see more clearly by making the object appear closer and hence making the angle between any two points on the object appear bigger. A refracting telescope (a refractor) is basically a combination of two lenses. The first lens (objective lens) is used to form an image near the focal point of the lens. The second lens (eyepiece) is used as a magnifying glass to examine the image. Figure 6 is a sketch of a refracting telescope. Properties of Light 8 Again, the telescope helps us to see more clearly by making the object appear closer and hence making the angle between any two points on the object appear bigger. It does not, however, make the image height bigger than the object height. (If we look at the moon, the image we see is NOT bigger than the real moon). Instead of using magnification as defined in Part 3, we need to define a magnifying power in terms of angles:

Museful = (coming from telescope) / (going into telescope) (8)

(See Figure 6 below.) Theoretically, (if the telescope is perfect - which ours in not) the magnification could be calculated:

Mtheoretical = fobjective lens / feyepiece (9) where the f's are the focal lengths of lenses.

f f objective lens eyepiece

 going into  coming f rom eye

objective lens eyepiece

Fig. 6. Refracting Telescope

PROCEDURE: 1. Look at either the millimeter markings or the sixteenth-of-an-inch markings on a ruler. Then gradually move the ruler away from you until you can no longer distinguish each marking. Measure the distance from your eyes to the ruler when you can just barely make out the individual markings.

2. Calculate the angle that your eye can just barely resolve using Eq. (6). The height of the object is either 1 mm or 1/16 inch, depending on which scale you used.

3. Use the "hall method" to determine the focal length of your second lens. The focal length of your second lens should be different for the focal length of the lens you determined in Part 3 above.

4. Place the lens with the smaller focal length near one end of the meter stick, and place the lens with the larger focal length at a distance approximately equal to the sum of the two focal Properties of Light 9 lengths away from the first lens. Look at something far away using this telescope by placing your eye near the smaller focal length lens, looking through it so that you also then look through the other lens. You may have to change the distance between the lenses slightly to obtain the best focus. (This part is hard to do. With a little patience you should see that this combination of lenses does indeed act like a telescope.)

5. After you have successfully completed step 4, look through your telescope at the ruler with the markings as in step 1 above. You may have to slightly change the distance between lenses to focus the telescope as the ruler is placed at different positions. What is your minimum angle that you can resolve with the telescope? [Calculate it just as you did in step 1.]

6. Calculate the experimental magnification of your telescope. To do this use Eq. (8) where

coming from is the angle you obtained in step 2 (the smallest angle you can resolve with your

eye by itself) and where going in is the angle you obtained in step 5.

7. Calculate the theoretical magnification of your telescope using Eq. (9) and the focal lengths of the two lenses you used.

8. Ideally, the two magnifications you calculated in steps 6 and 7 should be the same. What is not "ideal" about this experiment that might explain why these values are not exactly the same?

REPORT: Perform all of the calculations and answer all of the questions in the Procedure.