(b) By measuring the image height for various image distances (adjusted by sliding the tubes together or apart) a relationship can be determined.

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1 (c) The image is smaller, upright, virtual, ann the same side o the lens. Applying Inquiry Skills 7. (a) (b) By measuring the image height or various image distances (adjusted by sliding the tubes together or apart) a relationship can be determined. 0.3 MATHEMATICAL RELATIONSHIPS FOR THIN LENSES Investigation 0.3. Predicting the Location o Images Produced by a Converging Lens (Pages ) Purpose The purpose o this investigation is to determine the relationship between the ocal length, the image distance, and the object distance o a converging lens. Question What is the relationship between the ocal length, the image distance, and the object distance o a converging lens? Hypothesis/Prediction (a) It was expected that the relationship between the ocal length, the image distance, and the object distance o a converging lens would conorm to the ray diagrams or images produced by a converging lens developed previously. As the object was placencreasingly closer to the converging lens, it was predicted that the image would be ounncreasing urther rom the lens. Secondly, as the object drew closer to the lens, the image would become larger. It was expected that no image would be located when the object was placed at the principal ocus o the lens and when the object was placed between the lens and the principal ocus, a real image would not be projecten a screen. Instead, a virtual image, larger than the object itsel, would be seen on the same side o the lens as the object. This virtual image would be seen by looking through the lens rom the side opposite that o the object. Design An optical bench was used with a light bulb acting as an object. By placing the light bulb at various positions in ront o the converging lens o known ocal length, an image was sought in each case. Distances to the object anmage were measured and the characteristics o the image noted. 250 Unit 4 Light and Geometric Optics Copyright 2002 Nelson Thomson Learning

2 Materials converging lens ( = 0 cm 25 cm) small light source (miniature light bulb) translucent screen (white paper) optical bench Procedure Part : Real Image. With the converging lens positioned at the midpoint o the optical bench, the ocal lengt the lens was determined by locating the image o a distant object on the screen. The distance rom the lens to the screen was measured and recorded as the ocal lengt the lens. 2. The optical bench was turned end or end and the ocal length determined again, this time with the light entering the lens rom the other side. The average o the two values or the ocal length was calculated. 3. Using this value or the ocal length (), the object distances or 2.5, 2.0,.5,.0, and 0.5 were calculated and recorded in Table. 4. The light bulb, serving as the object, was placen the optical bench at 2.5. A screen was moved back and orth along the principal axis until a clearly ocusemage was observed. Its position anmage characteristics were measured and noten Table. 5. Step 4 was repeated or other object distances that resulten real images, namely 2.0 and Columns in Table or d, o d, and + i d were completed and the value o the reciprocal o the ocal length i was determined. 7. The magniication or the observations were calculated and recorded. Part 2: Virtual Image. The light bulb was placed at 0.5 and a pencil was held above the image as seen by looking through the lens rom the side opposite the object. The position o the pencil was adjusted until there was no relative movement o the pencil anmage when the observer s head was moved rom side to side. 2. The distance to the pencil rom the lens was measured and recorden Table as the image distance or this observation. The characteristics o the image were recorded. Observations The ocal lengt the lens was determined to be 0.0 cm in both attempts to measure it. In Part o this investigation it was noted that as the object got closer to the screen, the image got urther away. The image also got increasingly larger as the object drew nearer to the lens. In all cases, the image was ound to be inverted when compared with the orientation o the object. When the object was placed at.0, the ocal point, no image could be ound. Instead, a bright circular patc light could be seen on the screen, but no clearly ocusemage. This patc light was evident at all locations as the screen was moved back and orth along the principal axis. When the object was placed at 0.5, no image could be ounn the screen at any location. In Part 2 o this investigation, the image was locaten the same side o the lens as the object. It could be seen clearly by looking through the lens rom the side opposite the object. The image was larger and upright when compared to the object. The image distance in this case was assigned a negative value. Table Image Locations and Characteristics or Various Object Placements Observation Object Image Characteristics distance distance d () ( i) (cm) (cm) size attitude type (cm ) (cm ) + (cm ) Magniication (M) 2.5 = smaller inverted real = same inverted real = larger inverted real = 0.0 no image ound = larger upright virtual Copyright 2002 Nelson Thomson Learning Chapter 0 Lenses and the Eye 25

3 Analysis (b) The method or determining the ocal length as describen the procedure works because the rays o light arriving at the lens rom a distant object are travelling nearly parallel to eacther and to the principal axis. As such, they will all be reracted through the principal ocus o the lens, producing the image at this position. The more distant the object is, the more precisely the ocal lengt the lens can be determined. (c) The ocal lengths o the lens as measured rom both sides were ound to be identical. (d) As the object moved closer to the lens, the image got arther rom the lens and grew in size. The attitude o the image remainenverted. These observations held true or all object positions beyond the principal ocus. (e) It was not possible to locate a clearly ocusemage when the lens was placed at the principal ocus. () Provided the object was positioned beyond the principal ocus, a real image was always produced. When the object was placed between the principal ocus and the lens, a virtual image resulted. (g) The value o was determined as ollows: = 0.0 cm = 0.00 cm When this value is compared with the value o + or the cases involving real images, the values are ound to be do di the same. (h) I the distance to the virtual image is assigned a negative value as indicaten Table, then the values o and + are also equal. do di (i) The relationship between the ocal length, image distance, anbject distance or a converging lens can be expressed as a mathematical equation involving those three variables. Provided that object distances are always positive quantities, distances to real images are positive quantities, and distances to virtual images are always negative quantities, the ollowing expression holds true: = + do di Evaluation (j) The predictions made in this investigation were conirmed by the experimental results. The positions and characteristics o images or various object locations using a converging lens were ound to be in agreement with those predicted by the ray diagrams completed previously. In addition to those qualitative results, this investigation provided a mathematical ormula that deines the relationship between the ocal length, image distance, anbject distance or a converging lens. (k) The main source o experimental error in this investigation is the diiculty the observer has in deciding exactly where the image is most clearly ocused. The screen was moved back and orth along the principal axis until the image was judged to be clearest. All measurements were made in terms o the ocal lengt the lens which, itsel, was experimentally determined. I the ocal length was inaccurate, all other results would be as well. The ocal length was determined by ocusing the image o a distant object on a screen. To improve on the precision o this value, the object should be as ar away as possible. Having completed this investigation, it is apparent that when the object was located at 2.0, the image was ound to be exactly the same distance rom the lens on the opposite side. This result would provide an alternative metho determining the ocal lengt the lens. 252 Unit 4 Light and Geometric Optics Copyright 2002 Nelson Thomson Learning

4 PRACTICE (Page 37). Variable Situation when positive Situation when negative or a converging lens or a diverging lens always never real image virtual image object is above PA object is below PA image is above PA image is below PA M image is upright image is inverted 2. Page 362, question 3 (a) = 32 mm = 64 mm = 5 mm = M =.0 (b) = 32 mm = 52 mm = 5 mm = M =.6 (c) = 32 mm = 6 mm = 5 mm = + 32 = + 64 = 64 mm = + 32 = + 52 = 83 mm = + 32 = + 6 = 32 mm = 32 6 M = 2.0 Copyright 2002 Nelson Thomson Learning Chapter 0 Lenses and the Eye 253

5 2. Page 362, question 3 (a) = 32 mm = 64 mm = 2 mm = 2 64 M = 0.33 (b) = 32 mm = 32 mm = 2 mm = + 32 = + 64 = 2 mm = + 32 = + 32 = 6 mm = 6 32 M = 0.50 Section 0.3 Questions (Page 37). (a) By measurement, the height o the invertemage is 4 cm. (b) = 25.0 cm = 80.0 cm = 30.0 cm = = = = 36.4 cm 30.0 = = 3.7 cm The invertemage is 3.7 cm below the PA at a distance o 36.4 cm rom the lens. 254 Unit 4 Light and Geometric Optics Copyright 2002 Nelson Thomson Learning

6 2. (a) By measurement, the height o the image is 5.0 cm. (b) = 20.0 cm = 60.0 cm = 20.0 cm = = = 5.0 cm = 20.0 = = 5.00 cm The object has a height o 5.00 cm ans located 5 cm rom the lens on the same side as the image. 3. (a) = 0.0 cm = 0.2 cm = = = 50 cm The screen must be placed 5.0 cm away or a clear image. (b) = 2.5 mm = = 0.2 cm = 50 cm h =? i 2.5 mm = = 625 mm The height o the dog on the screen is 62.5 cm. 4. = 0.0 cm = 4.0 cm = = 2.0 cm (negative because it is inverted) =? = = = 2.0 = + di do = di 2.0di = 2.0di di = 5 cm do = 30 cm For a real image ( is positive), the image anbject are on opposite sides o the lens. The total distance between the object and the image is 5 cm + 30 cm = 45 cm. Copyright 2002 Nelson Thomson Learning Chapter 0 Lenses and the Eye 255

7 Applying Inquiry Skills 5. No, you could not use a diverging lens because a diverging lens can only produce a virtual image that cannot be captured on a screen. 0.4 THE HUMAN EYE AND VISION PRACTICE (Page 373). Eye part Function iris changes size to regulate the amount o light pupil hole through which light enters the eye cornea irst part o eye where most o the reraction takes place aqueous humour colourless, watery luid to help maintain the shape o the eye vitreous humour colourless, jelly-like luid to help maintain the shape o the eye lens a lexible lens that can accommodate to change the ocus retina carpet o light sensitive cells ciliary muscles muscles used to change the shape o the lens to ocus 2. Light that passes through the pupil is absorbed by the retina. Since very little light comes back out, it appears black. 3. Our eyes can adapt more quickly passing into bright light than going into a dark room. The constriction o the pupils is an active muscular action, while the dilation requires relaxing o the muscles. Making Connections 4. I only one eye is unctioning, we do not get two separate images o an object and are unable to determine the exact location o one object relative to another because we cannot see i it blocks out parts o other objects. Section 0.4 Questions (Page 374). Most o the reraction o light takes place at the cornea. This boundary has the largest dierence in indices o reraction. 2. We have two eyes that provide two slightly dierent images o any scene to our brain. The brain can analyze these images to igure out whicbjects are distant and which are close. The angle, size, and double images allow us to know how ar we are rom objects. 3. (a) 256 Unit 4 Light and Geometric Optics Copyright 2002 Nelson Thomson Learning

Refraction and Lenses

$Refraction and Lenses$ Reraction and Lenses The most common application o reraction in science and technology is lenses. The kind o lenses we typically think o are made o glass or plastic. The basic rules o reraction still apply