1. 3.2 Images formed by a convex lens
Lens on a watch
Image formation
Construction rules
Graphical construction of image formation
Check-point 2
Position and nature of images
Magnification
Check-point 3
The lens formula
Check-point 4 1 2 3 4 5 6
Book 3A Section 3.2 Images formed by a convex lens

2. Book 3A Section 3.2 Images formed by a convex lens
Lens on a watch
Have you seen this kind of watch before?
There is a lens over the date-display so that the date can be seen more easily.
What kind of lens is this?
Convex lens
Book 3A Section 3.2 Images formed by a convex lens

3. 3.2 Images formed by a convex lens
Simulation
3.1 How images are formed by a convex lens
Seeing an image formed by a convex lens
Expt 3a
Book 3A Section 3.2 Images formed by a convex lens

4. Book 3A Section 3.2 Images formed by a convex lens
Experiment 3a
Seeing an image formed by a convex lens
Place a convex lens 50 cm in front of a letter ‘F’ illuminated by a ray box.
Move a translucent screen on the other side of the lens to capture a sharp image.
Remove the screen and see if the image can still be observed.
Book 3A Section 3.2 Images formed by a convex lens

5. Book 3A Section 3.2 Images formed by a convex lens
Experiment 3a
Seeing an image formed by a convex lens
Put the lens 5 cm away from the letter ‘F’ and see if the image can still be observed.
3.1 Expt 3a - Seeing images formed by a convex lens
Video
Book 3A Section 3.2 Images formed by a convex lens

6. Book 3A Section 3.2 Images formed by a convex lens
1 Image formation
Convex lens can form real and virtual images.
a Real images
A small object is viewed through a convex lens.
Object Y P
Light rays from the object converge to point Y. If we look at the lens inside the region bound by the dotted lines (e.g. at P), a cone of rays will enter our eyes.
Book 3A Section 3.2 Images formed by a convex lens

7. Book 3A Section 3.2 Images formed by a convex lens
a Real images
Object Y P   Q
Since the rays cross at Y, our brain perceives the object at this position.  image at Y
 real image (as light rays really diverge from it)
We cannot see image at Q, as no light from the object enters our eyes.
Book 3A Section 3.2 Images formed by a convex lens

8. Book 3A Section 3.2 Images formed by a convex lens
a Real images
We can place a translucent screen at Y to capture the image for viewing from different directions.
Only real images can be captured by a screen.
If the screen is moved forwards or backwards,
a point on the object becomes a small patch of light on the screen
image blurred
Book 3A Section 3.2 Images formed by a convex lens

9. Book 3A Section 3.2 Images formed by a convex lens
1 Image formation
b Virtual images
An object is viewed through a convex lens placed very close to it.
Light rays from the object still diverge after passing through the lens.
Object P
Our brain perceives them by extending them backwards.
Book 3A Section 3.2 Images formed by a convex lens

10. Book 3A Section 3.2 Images formed by a convex lens
1 Image formation
b Virtual images
Extended rays meet at point Y Y
Object P
 Our brain perceives image there
Virtual image (as no light rays actually pass through Y )
Virtual images cannot be captured on a screen.
Book 3A Section 3.2 Images formed by a convex lens

11. Book 3A Section 3.2 Images formed by a convex lens
2 Construction rules
Let us first investigate how light rays are refracted when they pass through a convex lens.
Simulation
3.2 Refraction by a convex lens
Construction rules for a convex lens
Expt 3b
Book 3A Section 3.2 Images formed by a convex lens

12. Book 3A Section 3.2 Images formed by a convex lens
Experiment 3b
Construction rules for a convex lens
Direct a light ray at a convex lens along the directions as shown.
2. Observe how the ray passes through the lens.
3.2 Expt 3b - Construction rules for a convex lens
Video
Book 3A Section 3.2 Images formed by a convex lens

13. Book 3A Section 3.2 Images formed by a convex lens
2 Construction rules
From Expt 3b, we can summarize the construction rules for a convex lens:
Rule 1
For a ray parallel to the principal axis,
it is bent so that it passes through the principal focus F on the other side of the lens.
Book 3A Section 3.2 Images formed by a convex lens

14. Book 3A Section 3.2 Images formed by a convex lens
2 Construction rules
Construction rules for a convex lens:
Rule 2
A ray passing through the principal focus F ’ emerges parallel to the principal axis.
Rule 3
A ray passing through the optical centre travels straight on.
Book 3A Section 3.2 Images formed by a convex lens

15. 3 Graphical construction of image formation
Ray diagrams are useful for locating images formed by lenses and figuring out their nature.
We can use this symbol to represent convex lenses and apply the three construction rules.
Book 3A Section 3.2 Images formed by a convex lens

16. 3 Graphical construction of image formation
Steps for drawing a ray diagram for a convex lens:
Step 1
Draw the principal axis and convex lens.
Step 2
Mark F ’ and 2F ’ on the principal axis on one side and F and 2F on the other side.
(2F ’ = 2F = 2  focal length)
Book 3A Section 3.2 Images formed by a convex lens

17. 3 Graphical construction of image formation
Step 3
Draw the object as an arrow upright on the principal axis at the given position.
Book 3A Section 3.2 Images formed by a convex lens

18. 3 Graphical construction of image formation
Step 4
Draw rays (with arrows to indicate directions) from the tip using any two construction rules.
If the refracted rays cross, the intersecting point is the location of the real image of the tip.
Otherwise, use dotted lines for extending rays backwards to locate the virtual image.
Book 3A Section 3.2 Images formed by a convex lens

19. 3 Graphical construction of image formation
Step 5
Draw the real image as a vertical arrow.
Similarly, draw a dotted arrow as the virtual image.
Simulation
3.3 Construction rules for a convex lens
Example 1
Image formed by a convex lens
Book 3A Section 3.2 Images formed by a convex lens

20. Book 3A Section 3.2 Images formed by a convex lens
Example 1
Image formed by a convex lens
An object is placed between F ’ and 2F ’ from a convex lens. Four rays, p, q, r and s, from the object are incident on the lens.
(a) Complete the rays and locate the image.
(b) Is it a virtual or a real image?
Real.
Book 3A Section 3.2 Images formed by a convex lens

21. 3 Graphical construction of image formation
Parallel rays not parallel to the principal axis always converge to a point on the plane.
This plane passes through the focus and ⊥ principal axis
 focal plane
If a screen is placed on the focal plane, it can capture the image of distant objects.
Book 3A Section 3.2 Images formed by a convex lens

22. Book 3A Section 3.2 Images formed by a convex lens
Check-point 2 – Q1
Draw the rays of light after being refracted by the convex lens. Also mark the optical centre, principal axis and focal length of the lens.
principal
axis C f f
Book 3A Section 3.2 Images formed by a convex lens

23. Book 3A Section 3.2 Images formed by a convex lens
Check-point 2 – Q2
Which emergent light ray is correct?
Book 3A Section 3.2 Images formed by a convex lens

24. Book 3A Section 3.2 Images formed by a convex lens
Check-point 2 – Q3
(a) Complete the ray diagram.
Book 3A Section 3.2 Images formed by a convex lens

25. Book 3A Section 3.2 Images formed by a convex lens
Check-point 2 – Q3
(b) Complete the ray diagram.
Book 3A Section 3.2 Images formed by a convex lens

26. 4 Position and nature of images
Studying images formed by a convex lens
Expt 3c
Book 3A Section 3.2 Images formed by a convex lens

27. Book 3A Section 3.2 Images formed by a convex lens
Experiment 3c
Studying images formed by a convex lens
Set up the apparatus.
Start with a large object distance (i.e. u > 2f ).
Move the screen until a sharp image of is formed.
Repeat step 2 with smaller object distances.
Observe how the image changes.
3.3 Expt 3c - Studying images formed by a convex lens
Video
Book 3A Section 3.2 Images formed by a convex lens

28. 4 Position and nature of images
We describe the nature of an image by pointing out whether it is:
(a) inverted or erect
(b) magnified or diminished
(c) real or virtual
Expt 3c shows that:
the position and nature of the image changes with the object distance.
 use the construction rules to find them
Book 3A Section 3.2 Images formed by a convex lens

29. 4 Position and nature of images
Distant object (object position: at infinity)
Image position: on focal plane
Image nature: Real, inverted, diminished
Book 3A Section 3.2 Images formed by a convex lens

30. 4 Position and nature of images
Object position: beyond 2F ’
Image position: between F and 2F
Image nature: Real, inverted, diminished
Book 3A Section 3.2 Images formed by a convex lens

31. 4 Position and nature of images
Object position: 2F ’
Image position: 2F
Image nature: Real, inverted, same size
Book 3A Section 3.2 Images formed by a convex lens

32. 4 Position and nature of images
Object position: between F ’ and 2F ’
Image position: beyond 2F
Image nature: Real, inverted, magnified
Book 3A Section 3.2 Images formed by a convex lens

33. 4 Position and nature of images
Object position: F ’
Refracted rays are parallel, image formed at infinity (i.e. no image formed)
Book 3A Section 3.2 Images formed by a convex lens

34. 4 Position and nature of images
Object position: within F ’
Image position: same side of the object
Image nature: Virtual, erect, magnified
For a convex lens, the nature of the image depends on the distance of the object from the lens.
Simulation
3.4 Images formed by a convex lens
Book 3A Section 3.2 Images formed by a convex lens

35. Book 3A Section 3.2 Images formed by a convex lens
5 Magnification
Definition of magnification m:
height of image (image size)
height of object (object size) = hi ho = m
image distance
object distance = v u = or m
Book 3A Section 3.2 Images formed by a convex lens

36. Book 3A Section 3.2 Images formed by a convex lens
5 Magnification
When magnification > 1,
 the image is magnified
When magnification < 1,
 the image is diminished
When Magnification = 1,
 the image is of the same size
Example 2
Finding the image on graph paper
Book 3A Section 3.2 Images formed by a convex lens

37. Book 3A Section 3.2 Images formed by a convex lens
Example 2
Finding the image on graph paper
Object: 5 cm high, 15 cm from a convex lens
Focal length of convex lens = 10 cm
Find the position and magnification of the image.
Draw a ray diagram.
Image distance
= 6 × 5 = 30 cm v u = 30 15 = m
= 2
Book 3A Section 3.2 Images formed by a convex lens

38. Book 3A Section 3.2 Images formed by a convex lens
5 Magnification
Example 3
Viewing through a magnifying glass
Book 3A Section 3.2 Images formed by a convex lens

39. Book 3A Section 3.2 Images formed by a convex lens
Example 3
Viewing through a magnifying glass
Amy is using a convex lens to view the newspaper. The figure shows what she sees.
(a) Estimate the magnification of the image.
Magnification =
image size
object size 3 1 =
= 3
(b) State the nature of the image.
Virtual, erect and magnified.
Book 3A Section 3.2 Images formed by a convex lens

40. Book 3A Section 3.2 Images formed by a convex lens
Example 3
Viewing through a magnifying glass
(c) The lens is held at 5 cm from the page. Drawing a ray diagram find the focal length of the lens.
From the ray diagram,
focal length = 7.5 cm.
Book 3A Section 3.2 Images formed by a convex lens

41. Book 3A Section 3.2 Images formed by a convex lens
5 Magnification
Example 4
Refracting telescopes
Book 3A Section 3.2 Images formed by a convex lens

42. Book 3A Section 3.2 Images formed by a convex lens
Example 4
Refracting telescopes
Convex lenses are used in many imaging instruments. Usually two lenses are used instead of one since the overall magnification is much larger. E.g. two convex lenses of different focal lengths are used in a refracting telescope.
Book 3A Section 3.2 Images formed by a convex lens

43. Book 3A Section 3.2 Images formed by a convex lens
Example 4
Refracting telescopes
The telescope is adjusted so that the focal planes of the two lenses coincide. The image formed by the objective acts as the object of the eyepiece.
Book 3A Section 3.2 Images formed by a convex lens

44. Book 3A Section 3.2 Images formed by a convex lens
Example 4
Refracting telescopes
(a) When the telescope is used to view a star, where is the image formed by the objective?
On the focal plane of the objective lens.
(b) Hence, where is the image formed by the eyepiece?
At infinity.
Book 3A Section 3.2 Images formed by a convex lens

45. Book 3A Section 3.2 Images formed by a convex lens
Example 4
Refracting telescopes fo fe
(c) Magnification of the final image = ,
where fo and fe = focal lengths of objective and eyepiece respectively.
How to increase the magnification of the telescope?
Use an objective of longer focal length and an eyepiece of shorter focal length.
Book 3A Section 3.2 Images formed by a convex lens

46. Book 3A Section 3.2 Images formed by a convex lens
Check-point 3 – Q1
Complete the following table for a convex lens:
Object position
Image position
Nature of image
< F ’
Same side as the object
Virtual, erect, magnified
F ’
>F ’ and <2F ’
2F ’
> 2F ’
At infinity
At infinity
No image is formed
> 2F
Real, inverted, magnified 2F
Real, inverted, same size
>F ’ and <2F ’
Real, inverted, diminished
on focal plane
Real, inverted, diminished
Book 3A Section 3.2 Images formed by a convex lens

47. Book 3A Section 3.2 Images formed by a convex lens
Check-point 3 – Q2
The virtual images formed by a convex lens must be _________ than the object.
larger
Book 3A Section 3.2 Images formed by a convex lens

48. Book 3A Section 3.2 Images formed by a convex lens
Check-point 3 – Q3
A boy looks at a poster through a magnifying glass and sees a magnified erect image.
What happens to the image if he moves the lens closer to his eyes?
A It gets larger till it gets totally blurred
B It gets larger, keeping erect all the way.
C It gets smaller and becomes totally blurred.
D It gets smaller, keeping erect all the way.
Book 3A Section 3.2 Images formed by a convex lens

49. Book 3A Section 3.2 Images formed by a convex lens
6 The lens formula
Expt 3d
The lens formula
Book 3A Section 3.2 Images formed by a convex lens

50. Book 3A Section 3.2 Images formed by a convex lens
Experiment 3d
The lens formula
Set up the apparatus using a convex lens with a known f. Set u > f .
Move the screen until a sharp image is formed.
Record u and v.
3. Repeat step 2 with different values of u. Record the corresponding values of v.
Video
3.4 Expt 3d - The lens formula
Book 3A Section 3.2 Images formed by a convex lens

51. Book 3A Section 3.2 Images formed by a convex lens
6 The lens formula
From Expt 3d, we have the Lens formula: 1 u v f + =
can be applied to both real and virtual images
the ‘real-is-positive’ convention is used:
Focal length f
Object distance u
Image distance v
Real
Virtual
Sign + –
Book 3A Section 3.2 Images formed by a convex lens

52. Book 3A Section 3.2 Images formed by a convex lens
6 The lens formula
Let’s use lens formula to solve Example 2.
Substitute u = 15 and f = 10: 1 15 v 10 + = 1 15 v 10 – = 
 v = 30
m = v u 30 15 =
= 2
The same result is obtained!
Example 5
Focal length of a magnifying glass
Book 3A Section 3.2 Images formed by a convex lens

53. Book 3A Section 3.2 Images formed by a convex lens
Example 5
Focal length of a magnifying glass
Detective Holmes is investigating a crime scene.
He puts a convex lens 2 cm away from a wall.
image is erect
magnification = 3
Focal length of the lens = ?
Book 3A Section 3.2 Images formed by a convex lens

54. Book 3A Section 3.2 Images formed by a convex lens
Example 5
Focal length of a magnifying glass
u = 2 cm
m = 3
image is erect
m = v u
 v = mu = 3 × 2 = 6
The image is virtual (∵erect and magnified).
∴ Image distance should be taken as –ve. 1 u v f + = 1 2
(–6) + =
 f = 3
Focal length of the lens is 3 cm.
Book 3A Section 3.2 Images formed by a convex lens

55. Book 3A Section 3.2 Images formed by a convex lens
Check-point 4 – Q1
An object is placed 3 cm away from a convex lens.
If f = 6 cm, which of the following gives the best description for the image?
A virtual image, 6 cm away from the lens
B real image, 6 cm away from the lens
C virtual image, 3 cm away from the lens
D real image, 3 cm away from the lens
Book 3A Section 3.2 Images formed by a convex lens

56. Book 3A Section 3.2 Images formed by a convex lens
Check-point 4 – Q2
Determine the focal length of the convex lens. 1 u v f + = 1 4 12 + =
 f = 3
Focal length of the lens is 3 cm.
Book 3A Section 3.2 Images formed by a convex lens

57. Book 3A Section 3.2 Images formed by a convex lens
The End
Book 3A Section 3.2 Images formed by a convex lens