Chapter 19 Lenses (Sample)

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Judith Jacobs
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$scale, object size and distance 4. principal focus 5. at least 2 light rays 6. if convergent refracted rays: real image I at intersection 7.$ $if divergent refracted rays: virtual image I at intersection of extended rays Note: Arrows should be used to indicate the directions of travel of the rays.$

1 Chapter 19 Lenses (Sample) A. Key Examples of Exam-type Questions Problem-solving strategy How lenses produce images: Steps 1. principal axis 2. convex or concave lens 3. scale, object size and distance 4. principal focus 5. at least 2 light rays 6. if convergent refracted rays: real image I at intersection 7. if divergent refracted rays: virtual image I at intersection of extended rays Note: Arrows should be used to indicate the directions of travel of the rays. Use dotted lines for extended rays. Use solid lines for real images and dotted lines for virtual images. Example 1 An object PQ of height 4 cm is placed 2 cm in front of a lens L of focal length 6 cm as shown. An erect and magni ied image is formed. DSE-12-1B Q7 DSE-13-1B Q8

(1 mark) (ii) Draw a light ray to show how Tom can see P, the head of the object, through L. (1 mark) Solution (a) L is a convex lens.

2 2 Chapter 19 (a) What kind of lens is L? Explain your answer. (2 marks) (b) Complete the ray diagram on the igure and mark the image as P Q. Hence ind the linear magni ication of the image. (3 marks) (c) (i) On the igure, complete the light ray r to show how it travels after passing through L. (1 mark) (ii) Draw a light ray to show how Tom can see P, the head of the object, through L. (1 mark) Solution (a) L is a convex lens. (1A) Because only a convex lens can form an erect and magni ied image. (1A) (b) 1. Find the image distance from the intersection of the extended rays. 2. Find m using the ratio of the image distance to the object distance. The diagram: (2A)

$(1A) Note that the refracted ray should be traced back from Q, instead of P. (Reference: HKDSE report 2012) (ii) See the above diagram.$

3 Lenses (Sample) 3 The linear magni ication m = 3 2 = 1.5. (1A) Two correct rays to ind P Q : 2A Mind the use of dotted lines. Dotted lines are used for extended rays behind the object. (Reference: HKDSE report 2013) (c) (i) See the above diagram. (1A) Note that the refracted ray should be traced back from Q, instead of P. (Reference: HKDSE report 2012) (ii) See the above diagram. (1A) Tom is looking at the image, so the light ray appears to diverge from P instead of What-if How does the linear magni ication change when the object is approaching the lens? P. Ans: decreases

4 Chapter 19 Example 2 Mike investigates the image formation of a convex lens by placing an illuminated object and a screen on each side of the lens.

(Hint: consider x = 20 cm) (2 marks) (b) The object distance is now 60 cm. (i) what is the linear magni ication of the image? (1 mark) (ii) what is the nature of the image?

4 4 Chapter 19 Example 2 Mike investigates the image formation of a convex lens by placing an illuminated object and a screen on each side of the lens. A graph of y, distance between the object and the screen against x, object distance is obtained. AL-07-1A Q5 (a) What is the focal length of the lens? (Hint: consider x = 20 cm) (2 marks) (b) The object distance is now 60 cm. (i) what is the linear magni ication of the image? (1 mark) (ii) what is the nature of the image? (2 marks) (c) Find y when x = 5 cm. (2 marks) (d) Mike thinks that the centre of the image will be dimmer if the centre of the lens is covered by a small black paper. Comment on his statement. Solution (2 marks) (a) When x = 20 cm, the image distance is = 20 cm. (1M) Construct a ray diagram for the situation, the focal length f = 20/2 = 10 cm (1A) (b) (i) The image distance is = 12 cm. Therefore, the linear magni ication is 12 = 0.2. (1A) 60 (ii) inverted, real, diminished (2A) According to HKDSE report 2012, you can only get 2 marks even through there (c) Applying 1 are 3 image natures. f = 1 u + 1 v, we have 1 v = 1 f 1 u = = 0.1 v = 10 cm (1M) So, y = 10 5 = 5 cm. (1A) Take v as +ve when you calculate the value (d) He is incorrect (1A) of y. When part of the lens is covered, part of the light rays is blocked. The rest of the light rays would travel through the uncovered part and focus on the screen. As the light rays reaching the screen spread evenly on the screen, the whole image will be dimmer, instead of the centre of the image. (1A) According to the HKALE report 2007, quite a number of candidates made the What-if If x = 12 cm, what is the image distance and the linear magni ication similar mistake as Mike made. of the image? Ans: 60 cm; 5 (The answer can be easily obtained without using the lens formula.)

Lenses (Sample) 5 Example 3 Peter carries out an experiment to determine the focal length of a convex lens with the set-up shown.

(3 marks) (ii) What is the linear magni ication of the image formed when Peter determines the focal length of the lens?

(2 marks) (c) When Peter replaces the convex lens with another convex lens of shorter focal length, he notices that a diminished image is formed. (i) Why? Brie ly explain.

5 Lenses (Sample) 5 Example 3 Peter carries out an experiment to determine the focal length of a convex lens with the set-up shown. DSE-12-1B Q7 DSE-14-1B Q6 (a) (i) Describe how Peter can determine the focal length f of the lens. Illustrate your answer with a diagram. (3 marks) (ii) What is the linear magni ication of the image formed when Peter determines the focal length of the lens? (1 mark) (b) Can Peter measure the focal length of a concave lens using the above set-up? If yes, how? If not, why? (2 marks) (c) When Peter replaces the convex lens with another convex lens of shorter focal length, he notices that a diminished image is formed. (i) Why? Brie ly explain. (2 marks) (ii) Compare the brightness of this image with the image mentioned in (a)(ii). (2 marks) Solution (a) (i) The diagram: (2A) 1A for correct light rays to ind the image 1A for correct position of image The light rays coming from the head of the object should intersect at the head of the image. (Reference: HKDSE report 2014) The focal length of the lens is equal to the distance between the lens and the pin. (1A) (ii) The magni ication of the image is 1. (1A) (b) no (1A) The pin and its image formed are not on the same side of the lens. (1A)

6 6 Chapter 19 (c) (i) By the lens formula, 1 f = 1 u + 1. If f decreases, v decreases while v keeping u ixed. (1A) The lens is convex and the image is real, Therefore the linear magni ication decreases. (1A) therefore both f and v are +ve. (ii) This image is brighter than the previous one (1A) because the same amount of light spreads over the diminished image. (1A) The brightness of the image depends on the light energy received per unit area. (Reference: HKDSE report 2012) What-if How does the measured value of f change if the mirror is moved farther from the lens? Ans: no change B. Common mistakes made by Exam Sitters Focal plane and principal focus Light rays from different points at in inity should focus on different points on the focal length. Position of image see CE-10-2 Q14 see DSE-14-1B Q6 Parallel light rays converge to a point on the focal plane after passing through a convex lens. They converge to the principal focus only if they are parallel to the principal axis. Light from the head (tail) of the object focus on (or appear to diverge from) the head (tail) of the image. see CE-09-1 Q5 see DSE-12-1B Q7 Refracted light rays from the same point of an object converges to, or appears to diverge from, the corresponding point of the image.

Lenses (Sample) 7 Paths of light rays The light rays

Object and image positions Mind the positions of the

axis. Position of the lens see AL-05-2A Q9 see DSE-12-1A

positions for the lens to form a sharp image.

7 Lenses (Sample) 7 Paths of light rays The light rays should pass through the image (not stop at it). Object and image positions Mind the positions of the object and the image, they may not lie on the principal axis. Position of the lens see AL-05-2A Q9 see DSE-12-1A Q22 For a ixed object image separation, there are two positions for the lens to form a sharp image. One gives a magni ied image and the other one gives a diminished image. exception: f = d/2

8 Chapter 19 Magni ied images A convex lens can produce a magni ied

Pay attention to the nature of the image produced when answering

Reminders of Exam Syllabus Convex and concave lenses convex lens:

than the edge only thin lenses are discussed Terms optical centre C:

lens focal plane: parallel incident light rays converge to a point or

8 8 Chapter 19 Magni ied images A convex lens can produce a magni ied real image or a magni ied virtual image. Pay attention to the nature of the image produced when answering related problems. C. Reminders of Exam Syllabus Convex and concave lenses convex lens: central part thicker than the edge concave lens: central part thinner than the edge only thin lenses are discussed Terms optical centre C: centre of a lens principal axis: line through C; perpendicular to the lens focal plane: parallel incident light rays converge to a point or appear to diverge from a point of this plane principal focus F: intersection of the focal plane and the principal axis focal length f : distance CF a lens has two principal foci

Lenses (Sample) 9 Real images light rays intersect at X light rays come from the image position real image is formed at X Real image can be seen directly (inside a particular region).

9 Lenses (Sample) 9 Real images light rays intersect at X light rays come from the image position real image is formed at X Real image can be seen directly (inside a particular region). Our brains perceive that the object is located at X. Virtual images light rays seem to diverge from Y no light ray comes from the image position virtual image is formed at Y Virtual image can be seen directly (inside a particular region). Our brains perceive that the object is located at Y.

10 Chapter 19 Capturing images with screens Real images can be

Convex lens ray-tracing rules: object O, object distance u, image

parallel to the principal axis converge to F 3.

10 10 Chapter 19 Capturing images with screens Real images can be captured by a translucent screen but virtual images cannot. Convex lens ray-tracing rules: object O, object distance u, image I, image distance v 1. a light ray passes straight through C 2. parallel to the principal axis converge to F 3. through F parallel to the principal axis rules (2) and (3) are inverse: consider reversibility of light

Lenses (Sample) 11 nature of image: u v erect/inverted real/virtual image size v = f diminished u > 2f f

erect virtual magni ied Concave lens ray-tracing rules: 1. a light ray passes straight through C 2.

towards F parallel to the principal axis nature of image: erect, diminished and virtual The image must be

11 Lenses (Sample) 11 nature of image: u v erect/inverted real/virtual image size v = f diminished u > 2f f < v < 2f diminished inverted real u = 2f v = 2f same size f < u < 2f v > 2f magni ied u = f u < f v > u erect virtual magni ied Concave lens ray-tracing rules: 1. a light ray passes straight through C 2. parallel to the principal axis appear to diverge from F 3. towards F parallel to the principal axis nature of image: erect, diminished and virtual The image must be located between the focal plane and the lens Covering part of the lens If part of the lens is covered, the whole image can still be seen but it becomes dimmer.

12 Chapter 19 Linear magni ication m m = h i h o = v u for

lens u > 2f m < 1 u = 2f m = 1 u < 2f m > 1 concave lens all

image, the dimmer the brightness of the image.

v real-is-positive: v (virtual image): ve f (concave lens):

12 12 Chapter 19 Linear magni ication m m = h i h o = v u for convex and concave lenses, consider similar triangles convex lens u > 2f m < 1 u = 2f m = 1 u < 2f m > 1 concave lens all m < 1 Image size and brightness The larger the size of the image, the dimmer the brightness of the image. for a given object (same setting) Lens formula 1 f = 1 u + 1 v real-is-positive: v (virtual image): ve f (concave lens): ve otherwise: +ve f u v convex (real image) convex (virtual image) + + concave +

CHAPTER 3LENSES. 1.1 Basics. Convex Lens. Concave Lens. 1 Introduction to convex and concave lenses. Shape: Shape: Symbol: Symbol:

CHAPTER 3LENSES. 1.1 Basics. Convex Lens. Concave Lens. 1 Introduction to convex and concave lenses. Shape: Shape: Symbol: Symbol: CHAPTER 3LENSES 1 Introduction to convex and concave lenses 1.1 Basics Convex Lens Shape: Concave Lens Shape: Symbol: Symbol: Effect to parallel rays: Effect to parallel rays: Explanation: Explanation: