1. 3.3 Images formed by a concave lens
The peephole
Image formation
Construction rules
Graphical construction of image formation
Check-point 5
Position and nature of images
Magnification
Check-point 6
The lens formula
Check-point 7 1 2 3 4 5 6
Book 3A Section 3.3 Images formed by a concave lens

2. Book 3A Section 3.3 Images formed by a concave lens
The peephole
Have you ever look through the peephole?
How does the image look like?
erect, diminished
The peephole consists of a concave lens.
Why a concave lens is used?
to identify visitors and the environment
Book 3A Section 3.3 Images formed by a concave lens

3. 3.3 Images formed by a concave lens
Can concave lens also form both real and virtual images?
Simulation
3.5 How images are formed by a concave lens
Seeing an image formed by a concave lens
Expt 3e
Book 3A Section 3.3 Images formed by a concave lens

4. Book 3A Section 3.3 Images formed by a concave lens
Experiment 3e
Seeing an image formed by a concave lens
Look through the concave lens to see the image of a letter ‘F’ from a ray-box.
Try to capture a image by a translucent screen.
Repeat steps 1 and 2 with different object distances.
3.5 Expt 3e - Seeing images formed by a concave lens
Video
Book 3A Section 3.3 Images formed by a concave lens

5. Book 3A Section 3.3 Images formed by a concave lens
1 Image formation
Expt 3e shows that image formed by concave lens can never be captured on a screen.
 only virtual images formed
Light rays from the object always diverge after passing through the concave lens.
Our brain perceives an image at Y. No light rays actually pass through Y.
Book 3A Section 3.3 Images formed by a concave lens

6. Book 3A Section 3.3 Images formed by a concave lens
2 Construction rules
Simulation
3.6 Refraction by a concave lens
Expt 3f
Construction rules for a concave lens
Book 3A Section 3.3 Images formed by a concave lens

7. Book 3A Section 3.3 Images formed by a concave lens
Experiment 3f
Construction rules for a concave lens
Direct a light ray at a concave lens along the directions as shown.
2. Observe how the ray passes through the lens.
3.6 Expt 3f - Construction rules for a concave lens
Video
Book 3A Section 3.3 Images formed by a concave lens

8. Book 3A Section 3.3 Images formed by a concave lens
2 Construction rules
Construction rules for a concave lens:
Rule 1
A ray parallel to the principal axis is bent
so that it appears to come from the principal focus F’.
Book 3A Section 3.3 Images formed by a concave lens

9. Book 3A Section 3.3 Images formed by a concave lens
2 Construction rules
Construction rules for a concave lens:
Rule 2
A ray directed towards the principal focus F is bent parallel to the principal axis.
Rule 3
A ray passing through the optical centre travels straight on.
Book 3A Section 3.3 Images formed by a concave lens

10. 3 Graphical construction of image formation
The symbol used to represent concave lens in ray diagrams:
Steps for drawing a ray diagram for a concave lens:
Step 1
Draw the symbol of concave lens and the principal axis.
Book 3A Section 3.3 Images formed by a concave lens

11. 3 Graphical construction of image formation
Step 2
Mark F ’, 2F ’, F and 2F on the principal axis.
Step 3
Draw the object on the principal axis at the given position.
Book 3A Section 3.3 Images formed by a concave lens

12. 3 Graphical construction of image formation
Step 4
Draw rays from the tip of the object using any two of the construction rules.
Use dotted lines for extending rays backwards to locate the virtual image.
Book 3A Section 3.3 Images formed by a concave lens

13. 3 Graphical construction of image formation
Step 5
Draw a dotted arrow as the virtual image with its tail on the principal axis.
Simulation
3.7 Construction rules for a concave lens
Example 6
Image formed by a concave lens
Book 3A Section 3.3 Images formed by a concave lens

14. Book 3A Section 3.3 Images formed by a concave lens
Example 6
Image formed by a concave lens
Four rays, p, q, r and s, from the object are incident on a concave lens.
(a) Complete the rays and locate the image.
(b) Is it a virtual or a real image?
Virtual.
Book 3A Section 3.3 Images formed by a concave lens

15. 3 Graphical construction of image formation
Note:
Parallel rays that not parallel to the principal axis always appear to diverge from a point on the focal plane.
Book 3A Section 3.3 Images formed by a concave lens

16. Book 3A Section 3.3 Images formed by a concave lens
Check-point 5 – Q1
Draw the rays of light after being refracted by the concave lens. Also mark the optical centre, principal axis and focal length of the lens.
principal axis C f f
Book 3A Section 3.3 Images formed by a concave lens

17. Book 3A Section 3.3 Images formed by a concave lens
Check-point 5 – Q2
Which of the following incident rays is mentioned in the construction rules? A B
Book 3A Section 3.3 Images formed by a concave lens

18. Book 3A Section 3.3 Images formed by a concave lens
Check-point 5 – Q3
How to find the focus of the lens?
Step 1:
Draw ray A parallel to the principal axis from the tip of the object O.
Step 2:
After passing through the lens, ray A appears to come from the ________ and the extended part __________the tip of the image.
focus
touches
Book 3A Section 3.3 Images formed by a concave lens

19. Book 3A Section 3.3 Images formed by a concave lens
Check-point 5 – Q3
How to find the focus of the lens?
Step 3:
The point where the extended part crosses the ______________ is the focus.  F
principal axis
Book 3A Section 3.3 Images formed by a concave lens

20. 4 Position and nature of images
Images formed by a concave lens:
Distant object (position: at infinity)
Image position: on focal plane, same side
Image nature: Virtual, erect, diminished
Book 3A Section 3.3 Images formed by a concave lens

21. 4 Position and nature of images
Object position: between the lens and 
Image position: <F ’, same side
Image nature: Virtual, erect, diminished
Book 3A Section 3.3 Images formed by a concave lens

22. 4 Position and nature of images
From the results above, we can conclude that:
For concave lenses, the image is always virtual, erect and diminished.
Simulation
3.8 Images formed by a concave lens
Book 3A Section 3.3 Images formed by a concave lens

23. Book 3A Section 3.3 Images formed by a concave lens
5 Magnification
magnification m hi ho = v u
Example 7
Finding the image on graph paper
Book 3A Section 3.3 Images formed by a concave lens

24. Book 3A Section 3.3 Images formed by a concave lens
Example 7
Finding the image on graph paper
Object : 5 cm high, 15 cm from a concave lens
Focal length = 10 cm
Find the position and magnification of the image.
Draw a ray diagram on a graph paper.
Image distance
= 1.2 × 5 = 6 cm v u = 6 15 = m
= 0.4
Book 3A Section 3.3 Images formed by a concave lens

25. Book 3A Section 3.3 Images formed by a concave lens
5 Magnification
Video
3.7 Coin box
Images formed by a camera
Example 8
Book 3A Section 3.3 Images formed by a concave lens

26. Book 3A Section 3.3 Images formed by a concave lens
Example 8
Images formed by a camera
In a single-lens reflex camera, the distance between the lens and the image sensor can be adjusted so that objects at different places can be put into focus.
Object: 1.2 m in front of the camera
(a) Explain briefly what kind of lens A is.
It is a convex lens since real images are formed on the image sensor.
Book 3A Section 3.3 Images formed by a concave lens

27. Book 3A Section 3.3 Images formed by a concave lens
Example 8
Images formed by a camera
(b) Focal length of the lens = 200 mm
(i) Find the distance between the lens and the image sensor by drawing a ray diagram.
Distance = 1.2 × 200 = 240 mm
(ii) Find the magnification of the image.
Magnification = v u
240
1200 =
= 0.2
Book 3A Section 3.3 Images formed by a concave lens

28. Book 3A Section 3.3 Images formed by a concave lens
Example 8
Images formed by a camera
(c) Now, lens A is replaced with lens B (same type but with a different f ).
The magnification increases.
(i) How should the distance between the lens and the sensor change so that a clear image can be formed on the sensor?
∵Image distance  when magnification .
∴The distance between the lens and the sensor should be increased.
Book 3A Section 3.3 Images formed by a concave lens

29. Book 3A Section 3.3 Images formed by a concave lens
Example 8
Images formed by a camera
(c) (ii) In order to get a wider view, should lens A or B be used?
The smaller the m, the wider the view.
 lens A should be used.
(d) Compare the images formed by a convex lens and a concave lens if the object distance is 2f.
Convex lens: real, inverted, same size
Concave lens: virtual, erect, diminished
Book 3A Section 3.3 Images formed by a concave lens

30. Book 3A Section 3.3 Images formed by a concave lens
Check-point 6 – Q1
The images formed by a concave lens are always ____________ , __________ and ________________ .
virtual
erect
diminished
Book 3A Section 3.3 Images formed by a concave lens

31. Book 3A Section 3.3 Images formed by a concave lens
Check-point 6 – Q2
Complete the table for a concave lens:
Object position
Image position
Nature of image
Between lens and infinity
At infinity
Within F ’, same side as the object
Virtual, erect, diminished
On focal plane, same side as the object
Virtual, erect, diminished
Book 3A Section 3.3 Images formed by a concave lens

32. Book 3A Section 3.3 Images formed by a concave lens
Check-point 6 – Q3
What is the magnification of the image formed by the concave lens?
A 0.2
B 0.5
C 2
D 5
Book 3A Section 3.3 Images formed by a concave lens

33. Book 3A Section 3.3 Images formed by a concave lens
6 The lens formula 1 u v f + =
The lens formula also
applies to concave lenses.
In the ‘real-is-positive’ convention:
the focal length of a concave lens is –ve.
the image distance is always –ve as only virtual images are formed
Simulation
3.9 Lens formula
Book 3A Section 3.3 Images formed by a concave lens

34. Book 3A Section 3.3 Images formed by a concave lens
6 The lens formula
Apply the lens formula to solve Example 7.
Substitute u = 15 and f = –10: 1 15 v
–10 + = 1 15 v
–10 – =
 v = –6 
m = v u 6 15 =
= 0.4
The same results are obtained!
Finding the focal length using the lens formula
Example 9
Book 3A Section 3.3 Images formed by a concave lens

35. Book 3A Section 3.3 Images formed by a concave lens
Example 9
Finding the focal length using the lens formula
Object: 9 cm in front of the lens
Image: virtual, 3 cm from the lens.
(a) Find the focal length of the lens.
Applying the lens formula: 1 u v f + = 1 9 –3 + =
 f = –4.5
(b) What kind of lens is this?
The value of f is –ve
 concave lens
Book 3A Section 3.3 Images formed by a concave lens

36. Book 3A Section 3.3 Images formed by a concave lens
6 The lens formula
Example 10
View through a lens
Book 3A Section 3.3 Images formed by a concave lens

37. Book 3A Section 3.3 Images formed by a concave lens
Example 10
View through a lens
Sam is using a lens to view a piece of ruled-paper.
(a) State the nature of the image. What kind of lens is this?
The image is diminished and erect.
This is a concave lens.
(b) Estimate the magnification of the image.
Magnification =
image size
object size 1 2 =
= 0.5
Book 3A Section 3.3 Images formed by a concave lens

38. Book 3A Section 3.3 Images formed by a concave lens
Example 10
View through a lens
(c) Find the distance between the lens and the ruled-paper if the f = 6 cm.
m = v u
 v = mu = 0.5u
Substitute v = –0.5u and f = –6: 1 u v f + = 1 u
–0.5u –6 + = 
1 – 2 u 1 –6 = 
 u = 6
Book 3A Section 3.3 Images formed by a concave lens

39. Book 3A Section 3.3 Images formed by a concave lens
Check-point 7 – Q1
Put ‘+’ or ‘–’ signs in the appropriate boxes to represent their signs. +
Image distance of a real image
Image distance of a virtual image
Focal length of a convex lens
Focal length of a concave lens – + –
Book 3A Section 3.3 Images formed by a concave lens

40. Book 3A Section 3.3 Images formed by a concave lens
Check-point 7 – Q2
An object 30 cm from a concave lens produces a virtual image 15 cm from the lens.
What is the focal length of the concave lens?
A 30 cm
B 10 cm
C –10 cm
D –15 cm
Book 3A Section 3.3 Images formed by a concave lens

41. Book 3A Section 3.3 Images formed by a concave lens
The End
Book 3A Section 3.3 Images formed by a concave lens