Wave03 Lenses Completed - kotze223...1. This formula allows locating the image directly without...

New Senior Secondary Physics Compulsory: Wave Motion Chapter 3Lenses

CHAPTER 3LENSES

1 Introduction to convex and concave lenses

1.1 Basics

Convex Lens Shape: Symbol: Effect to parallel rays: Explanation:

Concave Lens Shape: Symbol: Effect to parallel rays: Explanation:


1.2 Standard Terminologies

Convex Lens

Concave Lens


[Concept] Which of the following ray diagrams are possible?

(a) (b) (c)

(d) (e) (f)

[Concept] A pair of parallel rays passes through a lens as shown.

(a) State the type of lens shown above. (b) Find the focal length of the lens.


2 Image formation

2.1 Basic construction rules

Rule 1: Incoming ray // to principal axis Convex

Concave

Rule 2: Incoming ray through C

Convex

Concave

Rule 3: Incoming ray through F

Convex

Concave


[Ray diagram][HKCEE] If F, F' are foci and C,C’ are both at a distance of two times the focal length from the lens, which of the following ray diagrams is/are correct?

A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1),(2) and (3) [Ray diagram][HKCEE]

In the above diagram, F,F'are the foci of the concave lens and AB is an incident ray. Which of the following paths best represents the emergent ray? A. P B. Q C. R D. S E. T


2.2 Image formation and nature of image

Example 1: Image formed by plane mirror Complete the ray diagram to locate the image. State the nature of the image.

Nature of image: Example 2: Image formed by convex lens Complete the ray diagram to locate the image. State the nature of the image.

Nature of image: Example 3: Image formed by concave lens Complete the ray diagram to locate the image. State the nature of the image.

Nature of image:


2.3 Image formed by convex lens

Case 1: Near object: closer than focus (u f< )

Case 2: Mid-range object ( 2f u f< < )

Case 3: Far object ( 2u f> )


Special Case 1.5: Object at focus (u f= )

Special Case 2.5: Object at 2F ( 2u f= )

Special Case 3.5: Very far object (u恭 )


Quick Summary of convex lens image

2.4 Image formed by concave lens

Case only 1: Object anywhere

2.5 Distinctive features of convex and concave lenses

Convex Concave

Real vs virtual

Erect vs inverted

Magnified vs diminished


[Determine lens][HKCEE]

Figure 5 shows a paper with some letters 'J' printed on it. The paper is placed behind a glass filled with water. Figure 6 shows the image of the letters formed by the glass of water. (a) State the nature of the image formed (erect or inverted, magnified or diminished, real or virtual). (2 marks) (b) Jason holds a lens in front of the paper in Figure 5 and finds that the image formed is of the same nature as that formed by the glass of water. (i) What kind of lens is held by Jason? (1 mark) (ii) Sketch a ray diagram to show how the image of the letters is formed by the lens. (3 marks)

05


3 Measuring focal length of a convex lens

Method 1: Using far object (as special case 3.5)

Procedures:

Method 2: Using plane mirror [HKCEE] When an object O is placed in front of a convex lens and a plane mirror as shown above, an image I is formed at the same position as the object. Which of the following statements is/are correct?

(1) The image I is real (2) The focal length of the lens is 10 cm (3) If the distance between the lens and the plane mirror is changed to 2 cm, the position of the image I remains unchanged. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1),(2) and (3)


Method3: Ray tracing [HKCEE] Using the apparatus in Figure 9, describe the procedures of an experiment to find the focal length of a cylindrical convex lens.

[Further questions: Can this method be used to find the focal length of a concave lens?]


[determine lens][HKCEE]

A lens is used to look at some print on a paper. The image of the word ' PHYSICS' is shown above. Which of the following statements is/are true? (1) The lens is a converging lens (2) The image lies between the paper and the lens (3) The image is real A. (2) only B. (3) only C. (1) and (2) only D. (1) and (3) only E. (1),(2) and (3)

[ray diagram][HKCEE]

In the figure above, F is the focus of the converging lens. Which of the five rays is incorrectly drawn? A. P B. Q C. R D. S E. T

[lens application][HKCEE] A magnifying glass is used to read some small print in a book. Which of the following statements is correct? A. The magnifying glass is a concave lens B. The image of the small print is real C. The object distance is greater than the focal length of the glass D. The image distance is shorter than the object distance E. The small print and its image are on the same side of the glass


[lens application][HKCEE] An illuminated letter ‘R’ is placed in front of a lens as shown below and an image is formed on a translucent screen. The object distance is 30 cm and the image distance is 20 cm.

Which of the following statements is/are correct? (1) The lens is a converging lens (2) The image is diminished

(3) The shape of the image seen by the observer is . A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1),(2) and (3)

[lens application][HKCEE] (refers to above question) If a piece of paper is used to cover one-half of the lens, which of the following describes the change in the image as seen by the observer? A. The whole image can still be seen but the image becomes dimmer. B. The whole image can still be seen and its brightness remains unchanged. C. Only half of the image can be seen and the image becomes dimmer. D. Only half of the image can be seen but its brightness remains unchanged. E. The whole image disappears.


[single lens camera][HKCEE] A cup is placed in front of a window, outside which is a distant building. Two photos P1 and P2 as shown below are taken with the same single-lens camera.

Which of the following ray diagrams correctly shows how the image I of the cup O is formed by the lens of the camera in photo P1?

[single lens camera][HKCEE] (refers to above question) Which of the following statements about the two photos must be correct? A. In P1, the images of the cup and the building are on different sides of the lens of the camera. B. In P1, the image of the cup is real while that of the building is virtual. C. On taking P2, the distance between the lens and the film of the camera is shorter than that on taking P1. D. After taking P1, the photographer has to move forward in order to take P2.


4 Linear magnification

Concept of linear magnification What is the linear magnification in this case?

Mathematical definition of linear magnification

Linear magnification by object/image distances


[magnification][HKCEE]

A student holds a magnifying glass close to his eye to look at some small print on a paper. The image of the letters "EX" is shown in Figure 4. The magnification is 3. (a) What kind of lens is used as a magnifying glass? (1 mark) (b) State the nature (real or virtual, erect or inverted) of the image. (2 marks) (c) The paper is placed at a distance of 8 cm from the lens. In Figure 5, AB represents the object, and p, q are incident rays. A scale of 1 cm representing 4 cm for the object distance is used. (i) Draw the refracted rays of p and q and the image of AB in Figure 5. (ii) From the ray diagram, measure (1) the image distance, (2) the focal length of the lens. (6 marks)


(d) If the paper is placed closer to the lens, how would the size of the image and the image distance be affected? Illustrate your answer with a ray diagram. (4 marks) (e) If the paper is moved away from the lens to a position beyond the focus, the student finds that a clear image cannot be observed. Explain briefly. (2 marks)


5 Lens formula

The formula

1 1 1u v f+ =

Symbols used: Notes: 1. This formula allows locating the image directly without drawing ray diagram. 2. This formula applies to BOTH convex and concave lenses, and ANY image nature, by using the

following sign convention:

u

v

f

[Challenging] Prove the lens formula (in a simple case of convex lens).


[lens formula][HKCEE modified] An illuminated object is placed at a distance 20 cm in front of a convex lens and a sharp image is formed on a screen at a distance of 16 cm from the lens. Calculate the focal length of the convex lens.

[lens formula][HKCEE modified] An illuminated object is placed at a distance 20 cm in front of a convex lens and a magnified image is formed at 10cm from the object. Calculate the focal length of the convex lens.

FINAL REMARKS

One of the most important applications of refraction of light is the use of lenses. This chapter focuses mainly on how the image is formed by a single lens. How to locate the image and what nature of the image will have.

This chapter is fairly straight forward. Students should master the skills of drawing ray diagrams including the symbols, arrows, dotted lines, construction rules and all that. You MUST use ruler to construct ray diagrams. Students should also know how to determine the focal length of a lens and some important optical instruments like projector, single lens camera and magnifying glass.

Although not frequently countered in examination, lens formula allows students to check their answer from ray diagrams. However, students should use the formula with care and follow exactly the sign convention.

In terms of examination skills, students should most aware about the ray diagram drawing techniques.

Wave03 Lenses Completed - kotze223...1. This formula allows locating the image directly without...

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