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Reflection and Refractionwith the Ray BoxO B J E C T I V E So Investigate for reflection from a plane surface, the dependence of the angle ofreflection on theangle of incidence.

o Investigate refraction of rays from air into a transparent plastic medium.o Determine the index of refraction of a plastic prism from direct measurement ofincident andrefracted angles of a light ray.

o Investigate the focal properties of spherical reflecting and refracting surfaces.E Q U I P M E N T L I S T. Ray box, 60.08 prism, plano-convex lens, circular metal reflecting surfaces. Converging lens, diverging lens, protractor, straightedge, compass. Sharp hard-lead pencil, black tape, several sheets of white paper

T H E O R YReflection

The reflection of light from a plane surface is described by the law of reflection, whichstates that theangle of incidence yi is equal to the angle of reflection yr.

The angles are measured with respect to a line perpendicular to the surface. Reflectionfrom a planemirror or a plane piece of glass are examples of the law of reflection.In Figure 40-1(a) several incident rays and reflected rays are shown for a plane surface.

The angle ofincidence yi is seen to be equal to the angle of reflection yr.

RefractionIn general, light rays incident on a plane interface will be partially reflected and partiallytransmitted intothe second medium. The transmitted ray undergoes a change in direction because thespeed of light isdifferent for different media. The ray is said to be refracted. This is illustrated in Figure40-1(b). The angleof incidence is y1, and the angle of refraction is y2.

The speed of light in a vacuum is c (_3.00_108m/s), the maximum possible speed oflight. For anymaterial the speed of light is v where v c. A quantity called the index of refraction n

for any medium is

defined by nc/v. Because v c, the only allowed values of n are n 1. The relationship(Snells law)between the angle of incidence y1 and the refracted angle y2 isn1 sin y1 n2 sin y2 Eq: 1When n1 > n2, Equation 1 implies that y1 < y2. This states that a ray going from amedium of a givenindex of refraction to one of a smaller index of refraction is bent away from the normal.If n1 < n2 then


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y1 > y2, and a ray going into a medium of larger index of refraction is bent toward thenormal.Focal Properties of Reflection and RefractionDescriptions of the focal properties of reflection from spherical mirrors are shown inFigure 40-2. Whenreflection takes place from a concave spherical surface, incident parallel rays are

converging and come toan approximate focus point. If R is the radius of curvature of the spherical surface, thefocal point is adistance f (called the focal length) from the vertex of the spherical mirror where fR/2.Incident parallelrays on a convex spherical mirror are diverging, but they appear to have come from apoint. The distancefrom the vertex of the mirror to that point is called the focal length, and its magnitude isgiven by fR/2.

The focal length is positive for a concave converging mirror and negative for a convexdiverging mirror.Reflection at Plane Surface Refraction at Plane Surface

n1 sin _1_n2 sin _2Ray 1 Ray 1

Ray 3 Ray 3

Normal

to Surface

Normal

to Surface

Ray 2 Ray 2

Reflecting Surface

n2_2n1_1

(a) (b)

(b) E X P E R I M E N T A L P R O C E D U R E(c) Reflection(d) 1. Use black tape to cover all of the slits from the ray boxexcept the central slit

to produce a single ray(e) to examine reflection and refraction from a plane surface.(f) 2. Place the 60.08 prism on a piece of white paper in the position shown in Figure

40-3(a). Draw a straight(g) line along the face of the prism and place a small dot in the center of the line as

shown.(h) 3. Place the ray box about 0.15maway from the prism and adjust the single ray

to strike the plane surface

(i)at the position of the dot at an angle of incidence estimated to be about 608.With a straightedge, draw a

(j) straight line in the direction of the incident ray and one in the direction of thereflected ray. This will

(k) produce the lines shown in Figure 40-3(b). Repeat this process two more times,once for an incident

(l) ray of about 458 and once for an incident ray of about 308 to produce the linesshown in Figure 40-3(c).


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(m) 4. At the point of the dot construct a perpendicular to the face of theprism. Extend all six of the lines

(n) showing the ray directions until they intersect at the point of the dot to producethe lines shown in

(o) Figure 40-3(d). Use a protractor to measure the incident angles and reflectedangles for each of the

(p) rays. Record all these angles (to the nearest 0.18) in the Data Table.(q)Refraction(r) 1. Place the prism on the paper as shown in Figure 40-4(a). Draw straight lines on

the paper along two(s) adjacent faces of the prism as shown in part (b) of the figure.(t) 2. Place the ray box about 0.15m away from the prism. Adjust the direction of the

ray box so that the(u) incident ray strikes one face of the prism at an angle of about 508 to a line drawn

normally (90 degrees)(v) to the prism face. Use a straightedge to draw a line in the direction of the

incident ray and one in the(w)direction of the refracted ray as shown in Figure 40-4(b) and Figure 40-5

(x) 3. Using a separate sheet of paper for each ray, repeat Steps 1 and 2 for twoother rays, one incident at an

(y) angle of about 608 with respect to the normal andthe other incident at about 708with respect to the normal.

(z) 4. Construct the lines tracing the path of each of the incident rays through theprism in the order of the

(aa) steps shown in Figure 40-5. This will produce a figure from which theangles y1, y2, y3, and y4 can be

(bb) determined with a protractor. Measure these angles for each of the threecases and record the values of

(cc) all four angles (to the nearest 0.18) in the Data Table.

(dd) Focal Properties of Reflection and Refraction(ee) 1. Remove the black tape from the ray box slits. Place the plastic plano-convex lens next to the slits to

(ff) produce five parallel rays from the ray box. The lens may have to be rotated justslightly to produce

(gg) the best set of parallel rays.(hh) 2. Place the circular metal reflector on a piece of white paper and trace its

outline on the paper. Place the(ii) ray box about 0.15m away on the concave side of the reflector. Align the five

parallel rays with(jj) the center of the reflector to produce a pattern like the one in Figure 40-2(a).

Make a tracing of this(kk) pattern, and from it, measure the focal length of the concave reflector.

Record it in the Data Table as fcon.(ll) 3. Turn the reflector around and repeat Step 2 on another piece of paper with the

reflector now acting as(mm) a convex mirror. Trace the pattern, which should look like that of Figure

40-2(b). Extend the reflected(nn) rays back to the point from which they appear to come. Measure the focal

length and record it in the(oo) Data Table as fdiv.


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(pp) 4. Using a compass, construct a circular arc that is the same radius ofcurvature as the reflector. Record in

(qq) the Data Table the radius of that constructed circle as R, the radius ofcurvature of the reflector.

(rr)5. Place the plastic converging and diverging lenses on separate pieces of paperand trace the ray pattern

(ss) produced by the parallel beam of rays from the ray box. Patterns likethose of Figure 40-3 should be

(tt)observed. Measure the focal length of the converging lens and record it in theData Table as fcon.

(uu) Measure the diverging lens focal length and record it in the Data Table asfdiv.

(vv) C A L C U L A T I O N S(ww) Reflection(xx) 1. Calculate the difference jyi_yrj between the measured values of the

incident and reflected angles for(yy) each of the three rays and record them in the Calculations Table.(zz) Refraction

(aaa) 1. According to Snells law, at the first surface (1) sin y1(bbb) n sin y2. The value of n1 has been used for air,(ccc) and n is the index of refraction of the prism. At the second surface, the

equation is n sin y3(ddd) (1) sin y4.(eee) Solving these two equations for n gives(fff) n sin y1(ggg) sin y2(hhh) and n sin y4(iii)sin y3(jjj)Eq: 2(kkk) These lines may have

(lll) to be extended some

(mmm) distance in either

(nnn) direction in order to

(ooo) measure the angles

(ppp) with a protractor.

(qqq) (a) (b) (c)

(rrr) _4(sss) _3_2(ttt) _1

2. Use these two equations to calculate two values of n for each of the incident rays.These are notindependent measurements because the errors made in drawing the rays to determinethe angle tendto produce two values of n with compensating errors. Take the average of the twovalues calculatedby Equation 2 as a single measurement and record in the Calculations Table theaverage value of n foreach ray.


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3. Calculate the mean n and standard error an for the three measurements of n andrecord them in theCalculations Table.Focal Properties of Reflection and Refraction1. Calculate the percentage difference between the value of fcon and the value of fdiv forthe reflector.

2. According to theory, the value of the focal length for the reflector should be equal toR/2. Calculatethe percentage difference between the measured value of R/2 and the focal lengths fconand fdiv for thereflector.COPYRIGHT

O B J E C T I V E So Investigate the properties of converging and diverging lenses.

o Determine the focal length of converging lenses both by a real image of a distantobject and byfinite object and image distances.

o Determine the focal length of a diverging lens by using it in combination with aconverging lensto form a real image.

E Q U I P M E N T L I S T. Optical bench, holders for lenses, a screen to form images, meter stick, tape. Lamp with object on face (illuminated object), three lenses (f_20,10,_30 cm)

T H E O R YWhen a beam of light rays parallel to the central axis of a lens is incident upon aconverging lens,

the rays are brought together at a point called the focal point of the lens. The distancefrom the centerof the lens to the focal point is called f the focal length of the lens, and it is a positivequantity for aconverging lens. When a parallel beam of light rays is incident upon a diverging lens therays divergeas they leave the lens; however, if the paths of the outgoing rays are traced backward,the rays appear


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to have emerged from a point called the focal point of the lens. The distance from thecenter of thelens to the focal point is called the focal length f of the lens, and it is a negative quantityfor a diverginglens. In Figure 41-1 two common types of lenses are pictured. In general, a lens isconverging or

diverging depending upon the curvature of its surfaces. In Figure 41-1 the radii ofcurvature of thesurfaces of the two lenses are denoted as R1 and R2. The relationship that determinesthe focal length f interms of the radii of curvature and the index of refraction n of the glass of the lens iscalled the lensmakers equation. It is1f n _ 1 1R1

_ 1R2

_Eq: 1For the converging lens shown in Figure 41-1(a) the radius R1 is positive and the radiusR2 is negative, butfor the diverging lens of part (b), the radius R1 is negative and the radius R2 is positive.

The signs of theseradii are determined according to a sign convention that is described in all elementary

textbooks.

As an example, consider a double convex lens like the one shown in part Figure 41-1(a)made fromglass of index of refraction 1.60 with radii of curvature R1 and R2 of magnitude 20.0 and

30.0 cm,respectively. According to the sign convention given above, that would mean R120.0cm andR2_30.0 cm. Putting those values into Equation 1 gives a value for the focal length f of20.0 cm.Essentially, Equation 1 indicates that a lens that is thicker in the middle than at theedges isconverging, and a lens that is thinner in the middle than at the edges is diverging. Alens can be classifieas converging or diverging merely by taking it between ones fingers to see if it isthicker at the center of

the lens than it is at the edge of the lens.Lenses are used to form images of objects. There are two possible kinds of images. Thefirst type,called a real image, is one that can be focused on a screen. For a real image, lightactually passes throughthe points at which the image is formed. The second type of image is called a virtualimage; light does notactually pass through the points at which the image is formed, and the image cannot befocused on a


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screen. Diverging lenses can form only virtual images, but converging lenses can formeither real imagesor virtual images. If an object is farther from a converging lens than its focal length, areal image is formed.If the object is closer to a converging lens than the focal length, the image formed is avirtual one.

Whenever a virtual image is formed, ultimately it will serve as the object for some otherlens system toform a real image. Often the other lens system is the human eye, and the real image isformed on the retinaof the eye.In the process of image formation, the distance from an object to the lens is called theobject distance p,and the distance of the image from the lens is called the image distance q. Therelationship between theobject distance p, the image distance q, and the focal length of the lens f is1p 1q 1fEq: 2Equation 2 is valid both for converging (positive f ) and for diverging (negative f )lenses. Normally theobject distance is considered positive. In that case a positive value for the imagedistance means thatthe image is on the opposite side of the lens from the object, and the image is real. Anegative value for theimage distance means that the image is on the same side of the lens as the object, andthat the image is

virtual.If a lens is used to form an image of a very distant object, then the object distance p isvery large. Forthat case, the term 1/p in Equation 2 is negligible compared to the other terms 1/q and1/f in that equation.For the case of a very distant object, Equation (2) becomes(a)R1 R2(b)fR1R2F

1q 1fEq: 3For this case, the image distance is equal to the focal length. This provides a quick andaccurate way to


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determine the focal length of a converging lens, but it is only applicable to a converginglens because theimage must be focused on a screen. A diverging lens cannot form a real image, and thistechnique will notwork directly for a diverging lens.If two lenses with focal lengths of f1 and f2 are placed in contact, the combination of the

two in contactacts as a single lens of effective focal length fe. The effective focal length of the twolenses in contact fe isrelated to the individual focal lengths of the lenses f1 and f2 by1fe 1f1 1f2Eq: 4Equation 4 is valid for any combination of converging and diverging lenses. If theindividual lenses f1 and f2are converging, then the effective focal length fe will also be converging. If one of thelenses is convergingand the other is diverging, then the effective focal length can be either converging ordiverging dependingupon the values of f1 and f2. If the converging lens has a smaller magnitude than thediverging lens, thenthe effective focal length will be converging. We can use this fact to determine the focallength of anunknown diverging lens if it is used in combination with a converging lens with a focallength shortenough to produce a converging combination.

E X P E R I M E N T A L P R O C E D U R EFocal Length of a Single Lens1. Place one of the three lenses in a lens holder on the optical bench and place thescreen in its holder onthe optical bench. Place the optical bench in front of a window in the laboratory andpoint the benchtoward some distant object. Adjust the distance from the lens to the screen until asharp, real imageof the distant object is formed on the screen. You will be able to form such an image foronly two ofthe three lenses. This experimental arrangement satisfies the conditions of Equation 3.

The measuredimage distance is equal to the focal length of the lens. Record these measured image

distances in DataTable 1 as the focal length of the two lenses for which the method works. Call the lenswith the longestfocal length A, the one with the shortest focal length B, and the one for which no imagecan be formed C.2. Place lens B in the lens holder on the optical bench and use the lamp with the objectpainted on its faceas an object. For various distances p of the object from the lens, move the screen until asharp real


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image is formed on the screen. For each value of p measure the image distance q from

the screen to the

lens. Make sure that the lens, the object, and the screen are at the center of theirrespective holders. Tryvalues for p of 20, 30, 40, and 50 cm, determining the value of q for each case. If these

values of p do notwork for your lens, try other values until you find four values that differ by at least 5 cm.Record thevalues for p and q in Data Table 2.Focal Length of Lenses in Combination1. Place lens A and lens B in contact using masking tape to hold the edges of the twolenses parallel.Measure the focal length of the combination fAB both by the very distant object methodand by thefinite object method. For the finite object method, just use one value of the objectdistance p anddetermine the image distance q. Record the results for both methods in Data and

Calculations Table 3.2. Place lens B and lens C in contact, using masking tape to hold the edges of the twolenses parallel.Repeat the measurements described in Step 1 above for these lenses in combination.Record the resultsin Data and Calculations Table 4.

C A L C U L A T I O N SFocal Length of a Single Lens1. Using Equation 2, calculate the values of the focal length f for each of the four pairsof objects andimage distances p and q. Record them in Calculations Table 2.2. Calculate the mean f and the standard error affor the four values for the focal lengthf and record themin Calculations Table 2.3. The mean f represents the measurement of the focal length of lens B using finiteobject distances.Compute the percentage difference between f and the value determined usingessentially infiniteobject distance in Data Table 1. Record the percentage difference between the twomeasurements inCalculations Table 2.Focal Length of Lenses in Combination1. From the data for lenses A and B, calculate the value of fAB from the values of p andq. Record thatvalue of fAB in Calculations Table 3. Also record in that table the value of fAB determined

by the verydistant object method.2. Calculate the average of the two values for fAB determined above. This average valueof fAB is theexperimental value for the combination of these two lenses.3. Using Equation 4, calculate a theoretical value expected for the combination of lensesA and B. Use thevalues determined in Data Table 1 by the distant object method for the values of fA andfB in the


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calculation. Record this value as (fAB)theo in Data and Calculations Table 3.4. Calculate the percentage difference between the experimental value and thetheoretical value for fAB.Record it in Data and Calculations Table 3.5. From the data for lenses B and C, calculate the value of fBC from the values of p andq. Record that value

of fBC in Data and Calculations Table 4. Also record in that table the value of fBCdetermined by thevery distant object method.6. Calculate the average of the two values for fBC determined above. This average valueis theexperimental value for the combination of these two lenses.7. Using the average value of fBC determined in Step 6 and the value of fB from Data

Table 1 for the focallength of B, calculate the value of fC, the focal length of lens C using Equation 4. Recordthe value of fCin Data and Calculations Table 4.

reflection and refraction.doc phy last2

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