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Optics-Optical InstrumentsUM Physics Demo Lab 07/2013

Pre-Lab QuestionWhat important optical property does a concave mirror share with a thin converging lens?

Caution-Warning: Today we will make and use optical instruments to view distant objects through outside windows. NEVER UNDER ANY CIRCUMSTANCES ATTEMPT TO VIEW THE SUN with any type of lens, mirror, or combination of lenses and mirrors, as eye damage is CERTAIN to occur.

Second Pre Lab QuestionGiven the extreme danger of attempting to view the sun directly using lenses and/or mirrors, describe a technique we have already demonstrated in the previous lab which would permit you safely view a projected image of the sun.

EXPLORATIONExploration Materials

Property of LS&A Physics Department Demonstration LabCopyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109

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Yard stick mirror mount2 51 mm square flat mirrorsRefracting telescope kit – objective, eyepiece, foam cylinder, cardboard ring in

red plastic cylinder, two cardboard tubesMicroscope stand—three magnetic thumb tacks + ½” steel washer5 ¼” diameter cosmetic mirror on stand (concave/flat)3 ¼” diameter cosmetic mirror on stand (concave/flat)Hand-held magnifying glass40 W “candle” lampPower strip for lampCalculatorClear plastic rulerMeter stickBusiness cardMicro fiber cloth for polishing mirrors and lenses

DefinitionsA converging lens is thicker in the center than at its edges.The reflective side of a concave focusing mirror will hold water like a bowl.

You will find diagrams illustrating a converging lens and a concave mirror at the end of this worksheet.

Instrument #1: Two Plane Mirrors

You have been provided with two plane mirrors attached to a yardstick with mounts that can be rotated to any desired angle by loosening the wing nuts which clamp the mounts to the yardstick, rotating the mirror to the desired angle and then gently tightening the wing nut until the mirror is just snugly held in place

1. Arrange the mirrors so that you can view the image in one mirror by looking into the other. Now adjust the angles so that you can see around a corner by looking at the image of the second mirror in the first.

A) What is this instrument called?

B) Draw two mirrors (represented as straight lines) in the diagram below so that a ray of light will follow the path shown. (Hint: Apply the Law of Reflection and sketch in the normal direction for each mirror as a dotted line first).


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Instrument #2: Two Converging Lenses I

You have been provided with an optical instrument kit which contains two lenses, two cardboard tubes, a thin cardboard ring and red plastic end covers for the tubes. The small “eyepiece” lens is mounted in a foam plastic ring along with a very small cardboard tube. For the following experiments we will orient this lens by specifying which way the cardboard tube should be pointed. Note that the small lens in the eyepiece can fall out if the eyepiece is dropped.

1. Focus an image of the front projection screen onto the blank side of the business card with the eyepiece lens (point the cardboard tube toward the screen) and measure the distance from the image (card) to the center of the lens with a centimeter ruler. Parallel light rays from the distant bright screen are being brought to a focus at this distance, the focal length of the lens. Record the measured focal length below and calculate its magnifying power in diopters (1/meters). Finally, measure the diameter of the lens and calculate its f/number. Show your calculations below.

Eyepiece LensFocal Length (cm)


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Eyepiece Magnifying Power (Diopters )

Eyepiece Lens Diameter (cm)

Eyepiece Lensf/number

2. Lay the business card on the table and place the tripod lens stand (washer + 3 magnetic thumb tacks) over the printed side of the card so some of the print is visible through the hole. Place the eyepiece on the tripod lens stand, with the cardboard tube facing upward, away from the business card. View the print on the business card through the cardboard tube of the eyepiece, close to your eye.

A) Describe the image (upright or inverted, magnified or original size).

B) Where is the print (object) located relative to the focal length of the lens (outside f, inside f or at f). Is this image real or virtual? Why? (Hint: This is review from the last lab).

C) The magnification for a thin lens used as a magnifier is easy to calculate as M = 25 cm/f where 25 cm is assigned as a standard comfortable eye-to-lens viewing distance. Calculate the magnification for the eyepiece and record it below. Show your calculation. A magnification of 2 is reported as 2X

3. Lay the business card on the table and place the tripod lens stand over the printed side of the card so some of the print is visible through the hole. Place the eyepiece lens on the stand with the cardboard tube facing downward, toward the business card and observe the print through the lens, this time much further from your eye.


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Eyepiece Magnification X


B) Where is the print located relative to the focal length of the lens (outside f, inside f or at f)? Is this image real or virtual? Why? (Hint: This is review from the last lab).

C) How does the object distance (distance of print from lens) compare with the focal length of the lens?

4. Now view the image produced by the eyepiece lens on the stand through the hand magnifier.


B) Where is the image from the lens on the stand (called the objective lens for this instrument) located relative to the focal length of the hand magnifier (outside f, inside f or at f)? Is the image formed by the lens on the stand real or virtual? Why?

C) Is the image an accurate representation of the print? If not, describe any distortion you may observe.

D) What instrument uses two lenses arranged in this way?

The distortion you observe in the image is due to the use of a spherical shape for the lens surfaces and is called spherical aberration (“spherical shape error”). Using lenses with a parabolic shape eliminates this distortion, but parabolic surfaces are much more difficult to make.

Instrument #3: Two Converging Lenses II1. Measure the focal length and diameter of the large lens from the

Refracting Optics Kit and record the focal length, diameter, magnifying power and f/number for this lens below. Show your calculations.


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Large LensFocal Length (cm)

Large Lens Magnifying Power (Diopters )

Large Lens Diameter (cm)

Large Lensf/number

Now assemble the large lens and the eyepiece into the cardboard tubes so that the large lens is at one end of the larger diameter cardboard tube covered by the cardboard ring, while the eyepiece is in the end of the smaller diameter tube, with the smaller cardboard tube inserted into the larger tube so that it can slide back and forth. The very small cardboard tube inside the eyepiece should be pointed out of the end of the smaller tube so you can look through it. There is an example of the assembled instrument available for you to copy, and your instructor can help you to assemble these parts correctly.

2. Looking through the very small cardboard tube, point the instrument out a window and focus an image of distant objects through a window by sliding the smaller cardboard tube in and out of the larger one.


B) Where is the distant object located relative to the focal length of the large lens (outside f, inside f or at f)? How does the object


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distance for the far away objects compare with the focal length of the large lens?

C) Where is the image from the large lens (called the objective lens for this instrument) located relative to the focal length of the eyepiece (outside f, inside f or at f)? Is this image from the large lens real or virtual? Why?

D) Is the image viewed through the instrument an accurate representation of the distant objects? If not, describe any distortion you may observe

E) What is this instrument called?

F) The magnification for this instrument can be calculated as the ratio of the focal length of the two lenses. Call the magnification M, the focal length of the large objective lens fo and the focal length of the eyepiece lens fe . A (+) sign is used to indicate an upright image and a (-) sign is used to indicate an inverted image. Using these principles, suggest a formula for the magnification of this instrument and record it below. (Hint: Based on the size of the image you observe, should the magnification be a number greater or less than 1?) Once you have developed your formula, check it with your instructor.


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G) Now use your formula to calculate the magnification of your instrument. Be sure to include the appropriate (+) or (-) sign.

A Converging Mirror

1. Examine the large diameter cosmetic mirror.

A. Examine an image of your face in each side of the mirror. Are the images the same? If not, describe how they are different.


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Instrument Magnification X

2. Point the mirror at a bright distant object, either the front projection screen or distant objects through an outside window. If you are using the projection screen, be sure that you are at least half way across the room from it. Using the blank side of the business card in your hand as a small screen, try to project an image onto the card

A. One side of the mirror is flat, the other concave (dished in like a bowl). Which side of the mirror will focus an image onto the card?

B. Describe the image (upright or inverted).

C. Where is the distant object located relative to the focal length of the converging mirror (outside f, inside f or at f)? How does the object distance for the far away objects compare with the focal length of the mirror?

D. Record the focal length of the focusing side of the mirror, the mirror diameter, f/number and diopter magnifying power for the mirror below. Show your calculations.

Converging MirrorFocal Length (cm)


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Converging Mirror Magnifying Power

(Diopters )

Converging Mirror Diameter (cm)

Converging Mirrorf/number

E. Does a converging mirror function in the same way as a converging lens? Explain.

F. Predict what you will observe on a distant wall if you place the candle lamp at the focal point of the converging mirror.

G. Test your prediction from part (F) by performing the experiment and describe your results. Given your observations, what practical applications can you suggest?

H. Recall the relationship between image distance, object distance and focal length we demonstrated for a thin converging lens:

1/i + 1/o = 1/fBased on your observations do you expect the converging mirrorto obey this relationship?


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I. Using the hand magnifier, project an image of the candle lamp onto a distant wall and carefully observe the colors present in the image. Are all the colors focusing to the same place on the image? Explain how replacing the objective lens of a telescope with a mirror could reduce this effect, called chromatic aberration (“color error”). (Hint: How does passing through glass affect the colors of the light?)

J. Converging mirrors have one disadvantage: they focus rays to an image on the same side as the object, so that your head will block the incoming light if you attempt to view the image at the focal point. Describe how a small diameter flat mirror could be used to overcome this problem and sketch your design below.


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Everyday Applications Household mirrors (plane and magnifying) Periscopes Lighthouses (can use a converging mirror) Flashlights (converging mirrors) and Searchlights (converging mirrors

or Fresnel lens) Theatrical Spot Lights (Fresnel lens or converging mirror) Astronomical Telescopes (refracting with an objective lens or reflecting

with an objective mirror—both use a refracting eyepiece) Solar Power (converging mirrors to gather solar energy)

APPLICATION

A Reflecting TelescopeMaterials

5 ¼” diameter cosmetic mirror on stand (concave/flat)3 ¼” diameter cosmetic mirror on stand (concave/flat)Hand-held magnifying glassEyepiece from Refracting Optics KitMicro fiber cloth for polishing mirrors and lenses

1. Place the large converging mirror on a table top so it can view distant objects through a window (the front projection screen may be used if a window is not available). Now place the small flat mirror on the table about 5” in front of the large converging mirror, angled upward so that you can view the flat mirror over the top of the converging mirror. Adjust the angles of the two mirrors so that you can see the image produced by the converging mirror projected onto the flat mirror. Your instructor can help you arrange this.

A. Describe the image (upright or inverted).


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B. Where is the object located relative to the focal length of the converging mirror (outside f, inside f or at f). Is this image real or virtual? Why?

C. Now view the image in the small flat mirror with the hand magnifier and describe the image (upright or inverted magnified or original size).

D. Record the focal length, magnifying power, diameter and f/number for the hand magnifier below. You already have these data from the last lab, but it only takes a minute to retake the measurements and recalculate if you need to.

Hand MagnifierFocal Length (cm)

Hand MagnifierMagnifying Power

(Diopters)

Hand Magnifier Diameter (cm)


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Hand Magnifierf/number

E. Using your previously derived formula for the magnification of a refracting telescope, calculate the magnification of this telescope using the focal length of the converging mirror and hand magnifier. Are we justified in using the same formula? Why?

F. Use the foam eyepiece from the cardboard telescope to view the image in the flat mirror (look through the cardboard tube end of the eyepiece). This can be tricky—ask your instructor for help. What happens to the magnification of the telescope? Does this make sense based on our formula for calculating the magnification of the telescope? (Hint: Compare the focal lengths of the hand magnifier and the eyepiece lens and see what effect this has on the magnification predicted by our formula).

Challenge Work:

1. You wish to look at your new shoes in a plane mirror mounted on the wall. The top of the mirror is even with top of your head as shown. Does the mirror need to extend all the way to the floor for you to be able to see your feet? Draw a ray from your eye to the mirror to your feet to justify your answer and be sure that the ray properly obeys the law of reflection at the mirror surface. Indicate the position of the mirror bottom on the drawing.


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Summary:

1. The Law of Reflection states that the angle of reflection is equal to the angle of incidence for a reflected ray of light. The angles are defined with respect to the direction perpendicular to the reflecting surface called the normal.

2. Images where the light actually emanates from the location of the image are called real images. Images where the light only appears to emanate from the image location but does not actually do so are called virtual images. The image of a lamp filament projected by a thin converging lens is real. The image in a plane mirror is virtual.

3. Two plane mirrors can be combined to form a simple periscope which allows the user to view images of objects from around a corner or below an obstruction.

4. If an object is placed inside the focal length of a thin converging lens, an upright magnified virtual image is observed. The angular magnification for the simple magnifier can be calculated as 25 cm/f.

5. If an object is placed just outside the focal length of a lens (called the objective) a real, inverted image is formed. Viewing this real image inside the focal length of a second simple magnifier (called the eyepiece) produces a magnified virtual image which remains inverted. This combination of two lenses is called a compound microscope. Short focal length objectives and eyepieces produce the greatest magnification.

6. Viewing the inverted real image formed by a long focal length objective lens with a second simple magnifier (eyepiece) produces a refracting telescope. As with the compound microscope, the final image is inverted and magnified. The magnification for this telescope is easily calculated as –fobjective/ feyepiece where the minus sign indicates that the overall image is inverted. Long focal length objectives and short focal length eyepieces produce the highest magnifications at the price of a narrow field of view.


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7. For a compound microscope, the object to be viewed is placed outside but very close to the focal point of the objective lens. For the refracting telescope, the object to be observed is very far away (“at infinity”). For a compound microscope, the highest magnification is achieved when both the objective and the eyepiece have short focal lengths (high diopter magnifications). By contrast, the highest magnifications for a refracting telescope are achieved with a long focal length (low diopter magnification) objective lens and a short focal length (high diopter magnification) eyepiece.

8. Light passing through a refractive medium such as glass is separated into its component colors, as demonstrated by the rainbow of colors that emerges when white light falls on a glass prism or water droplets, forming a rainbow. This phenomenon, called dispersion, is undesirable in a telescope requiring special coatings on the lenses to correct it. When dispersion is present in lenses it is called chromatic aberration—“color distortion”.

9. Concave mirrors with a spherical shape will focus parallel rays of light to a focal point in the same manner as a thin converging lens, this time on the same side of the mirror as the object. The focal length of the mirror is easy to calculate as ½ the radius of curvature of the mirror: f=1/2 R.

10.One method to reduce chromatic aberration and the absorption of light passing through a telescope is to use a focusing (concave) mirror for an objective rather than a lens. The most basic of these designs is called a Newtonian reflecting telescope in honor of its inventor, Isaac Newton.

11. A concave spherical mirror does not perfectly focus parallel rays to a single point. Rather, rays near the edge of the mirror focus shorter than those near the axis of the mirror (paraxial rays). This distorts the resulting image and is called spherical aberration. Thick lenses made with spherical surfaces also exhibit spherical aberration, giving rise to the “fish eye” distortion seen when using the lens as a magnifier.

12. Spherical aberration can be eliminated from the images formed by mirrors and lenses by using a parabolic shape for the curved surfaces, but parabolic surfaces are much harder to produce.

13. A thin corrective lens can also be used to correct telescopes for spherical aberration, allowing large, easy to produce spherical mirrors to produce sharp images. This technique produces a telescope called a “Schmidt Camera” in honor of the 19th century optician who developed the prescription for the corrective lens and successfully produced telescopes of this design.

ReflectionA wave is reflected when it is incident upon a material that redirects it outward. Reflected waves are redirected according to the law of reflection: the angle of incidence is equal to the angle of reflection. The angles of incidence and reflection are defined with respect to the direction normal (perpendicular) to the mirror surface as shown below.

The law of reflection holds for each of type of mirror, but the result it produces is different for each. The plane mirror creates an actual-size virtual image of the object which appears to be behind the mirror. Concave mirrors make incident plane waves diverge, and convex mirrors cause incident plane waves to converge. Both of these contribute to the distorted images of faces and bodies you see in carnival mirrors which often have both convex and concave regions on the same mirror.


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Figure 1: Plane Mirror

Figure 2: Concave (Converging) Mirror


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Figure 3: Convex (Converging) Lens

Telescopes

Figure 4: (a) Refracting Telescope;(b) Newtonian Reflecting Telescope


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Figure 5: Schmidt Astronomical Camera


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