Optics-Image Formation Lab · Web viewLay a printed page on the table and stand the meter stick up with the zero end of the meter stick on the page so you can measure the distance

Optics-Image FormationUM Physics Demo Lab 07/2013

Pre-Lab QuestionWhat physical process changes the direction of a ray of light as it passes through a thin lens?

EXPLORATIONExploration Materials40-Watt “candle” lamp on wooden basePower stripMesh stand for candle lampCookie sheet pinhole projectorWhite cardboard projection screenHand-held magnifying glass2 Meter sticksClear plastic ruler4 Large binder clips (support legs for pinhole projector and screen)Small rubber band

Definitions

A converging lens is thicker in the center than at its edges.A diverging lens is thinner at the center than at its edges.

You will find diagrams illustrating converging and diverging lenses and mirrors at the end of this worksheet.

Pinhole OpticsProperty of LS&A Physics Department Demonstration Lab

Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109

1. In the diagram below, the arrow represents an object (candle lamp) at some distance from a small hole in a screen, referred to as a “pinhole”. Behind the pinhole is a second screen where light passing through the pinhole will be intercepted and displayed as an image (cardboard sheet). The pinhole is represented as a small gap in an opaque pinhole screen (aluminum foil baking pan). Using your clear plastic ruler, trace a ray of light (straight line) from the tip of the arrow (A) through the pinhole until it intersects the image screen. Repeat this for light rays originating from the bottom of the arrow (C) and the middle of the arrow (B). Label the points corresponding to A, B and C on the image screen.

Based on this “ray tracing” analysis, draw the arrow head corresponding to the top of the object (A) for the image you have constructed on the image screen.Can a pinhole produce an image of the object? Will the image be upright (“right-side-up”) or inverted (“up-side-down”)? How do you know this?

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

2. Set up your pinhole projector (aluminum foil pan) image screen (cardboard screen) and candle lamp to project an image of the lamp onto the screen as shown in the diagram for part 1. A wire mesh pedestal is provided to raise your lamp to the proper height and the large binder clips serve as the support legs for your projector and screen. Before you turn on your lamp (using the switch on the power strip) observe the orientation of the wire lamp filament so you can determine if the images produced by the three pinholes (small, medium and large) in the projector plate are upright or inverted. Now turn on the lamp and observe the three images.

A) Are the images upright or inverted?

B) Which pinhole (small, medium, large) produces the brightest image?

C) Which pinhole (small, medium, large) produces the clearest (best focused) image?

D) Which pinhole (small, medium, large) produces the dimmest image?

E) Which pinhole (small, medium, large) produces the most poorly focused image?


F) State the relationship between the quality of focus and brightness for the image produced by a pinhole.

3. Now trace three rays from top of the arrow “object” (point A) through the pin hole. One ray should pass through the top edge of the pinhole, one through the center of the pinhole and one through the bottom edge of the pinhole.

A) Do all the rays you have drawn intersect the image screen at the same place? Can the pinhole produce an image of the point at the tip of the object (arrow) at one exact point on the image screen?


B) An ideal pinhole is a geometric point with no physical size. Real pinholes must have some size (diameter) associated with them since no light can pass through a true geometric point, which has zero area. Based on your ray tracing above, how does the diameter of the pinhole affect the quality of the focus for a real pinhole?

C) Is this result (B) consistent with the pinhole images you observe with your projector? Explain the relationship between pinhole size, image brightness and quality of focus.

4. The depth of field is defined as the range of distances from a lens or pinhole where all objects are brought to a clear focus at the image screen (focal plane). Move the lamp back and forth and observe the clarity of focus for the images projected by the pinholes on the screen.

A) Based on your observations, how would you characterize the depth of field for a pinhole (large or small)? Explain how your observations support this characterization.


5. The magnification of a lens or pinhole is defined as the ratio of the image height to the object height, which by similar triangles can easily be shown to be equivalent to the ratio of the image distance (distance from pinhole to the image screen) and the object distance (distance from the pinhole to the object-in this case the lamp filament). In optics this is written as M= -(i/o) where the minus sign is included to signify that the image is inverted (up-side-down) relative to the object.

Start with the screen and the lamp at equal distances (15 cm ~ 6”) from the pinhole screen.

A) How do the sizes of the images compare with the size of the glowing filament in the lamp (the object)?

B) Decrease the object distance o by moving the lamp toward the pinhole screen. What happens to the size of the images? How is this consistent with the magnification equation?

C) Now increase the object distance o by moving the lamp away from the pinhole screen. What happens to the size of the images? How is this consistent with the magnification equation?


Optics of a Thin Converging Lens

Real Images and Focal Length

1. Focus an image of a distant lamp onto the wall with the magnifying lens and measure the distance from the image (wall) to the center of the lens with a meter stick. Parallel light rays from the distant lamp are being brought to a focus at this distance, which we will call the focal length of the lens. Record the measured focal length below.

Magnifying LensFocal Length (cm)

2. After discussing it with your group, predict what you will observe if you shine a lamp located at the focal point of the lens through the lens onto a distant wall.

3. Perform the experiment described in (2): place the candle lamp at the focal point of the lens and shine it on a distant wall. What do you observe?


4. Give an example of a practical application of the optical effect you demonstrated in (3). (Hint: We live near the world’s largest fresh water ocean, the Great Lakes. This technique had been used since the 19th century to guard the safety of ships on the Great Lakes and is still in limited use today).

5. A ray tracing analysis similar to the one you did for the pinhole yields the following relationship (known as the Thin Lens Equation) between the image distance i, the object distance o and the focal length f of a thin lens:

1/i + 1/o = 1/f

A) Lay two meter sticks end to end. Place the candle lamp at the zero of the first meter stick and the cardboard screen at a distance of 1.5 meters from the candle lamp. Starting with the magnifying lens at the screen, move it toward the lamp until you project an image of the lamp onto the screen. Record the image and object distances below. Now calculate the focal length of the lens using the thin lens equation and compare it to the focal length you have already measured. Show your calculation.


Image Distance (cm)

Object Distance (cm)

Calculated Focal Length (cm)

Previously Measured Focal Length (cm)

B) Now continue to move the lens toward the lamp until you find a second point where you can project an image of the lamp on the screen. Record the image and object distances below and again calculate the focal length.

Image Distance (cm)

Object Distance (cm)

Calculated Focal Length (cm)

Previously Measured Focal Length (cm)

C) How do the image and object distances for the second image you found (lens near the lamp) compare with the image and object distances you found for the first image (near the screen)? Does the thin lens equation predict this? (Hint: What happens to the focal length in the thin lens equation if the image and object distances are interchanged?)

D) The f/number of a lens is defined as the ratio of its focal length to its diameter. Measure the diameter of your lens in centimeters and calculate the f/number of the magnifying below (show your calculation):


f/number = Focal Length/Diameter = f/ ______

Virtual Images

1. Mark the location of the focal length of the magnifying lens on a meter stick by putting a small rubber band around it. Lay a printed page on the table and stand the meter stick up with the zero end of the meter stick on the page so you can measure the distance of the magnifying lens from the page as you move the lens up and down.

A) View the printing through the magnifying glass as you move the lens toward and away from the page. Compare the quality of focus for the image you observe for distances less than the focal length to the quality of focus for distances greater than the focal length. For what range of distances do you see a well-focused, magnified image of the printing?

B) Is the image upright or inverted?

C) The image distance for this virtual image is defined as negative, since the image appears to be on the same side of the lens as the object. Does the magnification equation M= -(i/o) predict the correct orientation for the image (upright=positive magnification, inverted=negative magnification)? How?


Everyday Applications Household mirrors (plane and magnifying) Lighthouses Indoor lighting Flashlights (converging mirrors) Slide projectors Reading glasses Cameras

APPLICATIONMaterialsDesk lamp with 100 watt soft white bulb (“slide projector” light source)Transparency-film “slide”Hand-held magnifying glassMeter stickReading glasses

1. The next experiment uses the desk lamp with a 100 watt light bulb as a bright light source. The lamp will get very hot in use, so please be careful to avoid touching the hot steel lamp shade and turn the lamp off when not in use.

A) Using the 100 watt desk lamp as a light source, project an image of your transparency film slide onto a distant wall with your magnifying lens. Sketch the arrangement of the light, slide and lens below. At what specific distance must the slide be from the lens to be projected clearly onto the wall? Is the image of the slide upright or inverted?


2. As you did for your magnifying lens, focus an image of a distant lamp onto the wall with the reading glasses and measure the distance from the image (wall) to the center of the lens with a meter stick. Record this measured focal length below.

Reading GlassesFocal Length (cm)

Opticians define the “Magnifying Power” of a lens in units of Diopters:

Magnifying Power (Diopters) = 1/(focal length in meters).

Note that this “Magnifying Power” is different than the magnification since it does not depend on image or object distances and in fact is just an alternate way of specifying the focal length of a lens. It has the advantage that magnifying power increases with decreasing focal length and therefore correctly predicts a stronger correction to vision with shorter focal length lenses.

A) Using your measured focal length, calculate the magnifying power of the reading glasses and compare it to the number printed on the glasses. Show your calculation and be sure to convert the measured focal length to meters! How well does your measured magnifying power compare with the value printed on the glasses?


Calculated Reading Magnifying Power

For Reading Glasses

(Diopters)

_______________

Labeled Magnifying

PowerFor Reading

Glasses(Diopters)

_____________

Challenge Work:

1. The top diagram shows a typical camera. The shutter, which opens and closes the lens to light from the outside, is not shown. The bottom diagram depicts two nearly identical cameras. The only difference between the two bottom cameras is that their lenses differ in f/number. Since they both have the same focal length f, the difference between the two cameras is that the


f/3 lens has a larger diameter than the f/22 lens. For your answers refer to the cameras as the f/3 camera and the f/22 camera.

A) Which has the greater depth of field? (Hint: Which lens is more like a pinhole?)

B) Which camera allows more light to enter and expose the film when the shutter is open?

C) The exposure time is defined as the amount of time that the shutter of the camera remains open to expose the film to light. Based on your answer to (B) and assuming the same available light, which camera can photograph the object with the shortest exposure time?

D) Photographers refer to lenses with low f/numbers such as the f/3 lens as “fast” lenses. Explain why this makes sense in light of your answers to (B-C) above.

2. The focal length for a pinhole is defined as the distance from the pinhole to the image screen. Calculate the f/number for a 1 millimeter diameter pinhole located a distance of 5 centimeters from an image screen. Show your work


and be sure to use consistent distance units (focal length and diameter both expressed either in millimeters or centimeters).

f/number = Focal Length /Diameter = f/ ______

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. Ray tracing demonstrates that pinholes can produce an inverted, real image. Small pinholes produce well focused, dim images. Large pinholes produce bright, poorly focused images. The depth of field for a point pinhole is infinite, and real pinholes have a very large depth of field. The f/number of a pinhole or lens is defined as the ratio of its focal length to its diameter. The focal length of a pinhole is the distance from the pinhole to the image screen. A true pinhole (geometric point) therefore has an “infinite” f/number (f/∞) (owing to a zero diameter) and real pinholes have very large f/numbers.

4. Convex lenses can focus parallel light rays to a common focal point and can therefore produce real images. Concave lenses always produce diverging rays and can only produce virtual images.

5. The speed of light in a material such as glass, water or plastic is slower than it is in vacuum. The ratio of (speed of light in vacuum)/(speed of light in matter) is called the refractive index of the material.

6. The direction of a light ray changes as it enters a material with a higher refractive index such that its angle with the normal decreases. This is how lenses change the direction of light rays and is described by Snell’s Law.

7. The Thin Lens Equation relates the image distance (i), object distance (o) and focal length (f) for a thin lens and is stated as: 1/i + 1/o = 1/f. This equation predicts that light from very distant objects (0→∞) will converge to form a real image at the focal point of a converging lens and that interchanging the image and object distances will again result in a focused image. It also predicts that an object placed at the focal point of the lens


(o=f) will project an image “to infinity” (1/i→0 so i→∞), that is, to a very distant screen (slide projector). Real images produced by a thin converging lens are inverted (“upside-down”) Objects viewed with image distances less than the focal length of the lens will produce an upright (“right-side-up”) virtual image of the object—this how a converging lens is used as a “magnifying glass”. The thin lens equation also works for diverging lenses which have a negative focal length.

8. The magnification for any thin lens or pinhole is defined as –(i/o) where the minus sign predicts that real images are inverted and virtual images (which have negative image distances) are upright.

9. The speed of light, and hence the index of refraction, is different in optical materials such as glass or plastic for different wavelengths of light. This effect is called dispersion. Blue light (short wavelength) is refracted (bent toward the normal) more than red light (long wavelength). This is how a prism separates white light into its component colors.

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.

Figure 2: Plane MirrorProperty of LS&A Physics Department Demonstration Lab

Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109

Figure 3: Concave (Converging) Mirror

Figure 4: Convex (Diverging) Mirror


Figure 5: Convex (Converging) Lens

Figure 6: Concave (Diverging) Lens


Documents

Optics-Image Formation Lab · Web viewLay a printed page on the table and stand the meter stick up with the zero end of the meter stick on the page so you can measure the distance