Bài giảng Lenses

	 Lenses 
1	 In daily life, you may have come across lenses that are thicker or thinner in the middle. 
Which of the following items do you think may contain lenses ? 
Eyeglasses. 
Peep-hole. 
Watch. 
Camera. 
Magnifying glasses. 
Security mirror. 
 
 
 
 
 
2	 When you see through lenses, 
	do the objects appear the same as they 	are? 
No ! 
Introduction 
 Lenses are very useful. 
e.g. in cameras, projectors, telescopes, microscopes and eyes 
 The most common lenses: 
 spherical lenses 
( i.e. the surface is spherical ) 
1	 Convex and concave lenses 
Convex lens - thicker at the centre than at the edge. 
1	 Convex and concave lenses 
Concave lens - thinner at the centre than at the edge. 
1	 Convex and concave lenses 
a	Converging or Diverging? 
convex lens 
( converging lens) 
concave lens 
( diverging lens) 
1	 Convex and concave lenses 
convex lens 
( converging lens) 
concave lens 
( diverging lens) 
a	Converging or Diverging? 
1	 Convex and concave lenses 
a	Converging lens 
You may remember ‘ con verging ’ as ‘ con centrating ’. 
bend the light inwards 
1	 Convex and concave lenses 
a	Diverging lens 
You may remember ‘ div erging ’ as ‘ divi ding ’. 
bend the light outwards 
1	 Convex and concave lenses 
a	Converging or diverging? 
Light converges or diverges as some parts of the wavefronts lag behind. 
converges 
diverges 
Recall that light travels more slowly in glass than in air. 
Refracted rays meet at a point called the principal focus F . 
principal focus 
 Parallel rays are refracted inwards . 
b	Key features of lenses 
Centre of the lens is called the optical centre C . 
optical centre 
F 
The distance of F from C is the focal length f of the lens. 
focal length 
F 
C 
 A convex lens has 2 principal foci . 
 1 on each side 
F 
F' 
The line through the optical centre and 2 foci is called the principal axis . 
principal axis 
F 
F' 
C 
Refracted rays appear to spread from a point called the principal focus F . 
 Parallel rays are refracted outwards . 
principal focus 
F 
optical centre 
Centre of the lens is called the optical centre C . 
F 
focal length 
The distance of F from C is the focal length f of the lens. 
C 
F' 
F 
F' 
F 
 A concave lens has 2 principal foci . 
 1 on each side 
The line through the optical centre and 2 foci is called the principal axis . 
principal axis 
C 
Q1 	 A light ray is incident on a 
A light ray is incident on a convex lens. 
Which one represents the path of the light ray? 
A	Path X . 
B	Path Y . 
C	Path Z . 
X 
Y 
Z 
Q2 	 A light ray is incident on a 
A light ray is incident on a concave lens. 
Which one represents the path of the light ray? 
A	Path X . 
B	Path Y . 
C	Path Z . 
X 
Y 
Z 
Seeing images formed by a lens 
Video 
2	 Image formation by a lens 
When the light from a point of an object enters our eyes, 
we can see the point . 
O 
I 
screen 
2	 Image formation by a lens 
a	Real images 
O 
I 
Light rays converge to a point. 
Image can be captured by a screen. 
screen 
O 
I 
Hence called ‘ real ’. 
2	 Image formation by a lens 
2	 Image formation by a lens 
Light rays diverge from a point. 
b	Virtual images 
O 
I 
convex lens 
No rays actually come from the image. 
Hence called ‘ virtual ’. 
2	 Image formation by a lens 
Light rays diverge from a point. 
b	Virtual images 
O 
I 
concave lens 
screen 
O 
I 
Since only convex lenses converge light rays, real images can only be formed by convex lenses. 
Light rays through lenses 
Video 
Video 
Simulation 
Simulation 
Video 
3	 Graphical construction of image formation 
a	Construction rules 
In ray diagrams, we use symbols to represent lenses. 
convex lenses 
concave lenses 
Construction rules for convex lenses 
A ray parallel to the principal axis... 
 is refracted through F . 
C 
F 
Rule 1 
F' 
C 
F 
A ray passing through F' ... 
 is refracted parallel to the principal axis . 
Rule 2 
Construction rules for convex lenses 
F' 
C 
F 
A ray passing through C ... 
 travels straight on. 
Rule 3 
Construction rules for convex lenses 
 is refracted so that it appears to come from F' . 
C 
F' 
F 
Construction rules for concave lenses 
A ray parallel to the principal axis... 
Rule 1 
C 
F' 
F 
Rule 2 
A ray directed towards F ... 
 is refracted parallel to the principal axis . 
Construction rules for concave lenses 
A ray directed towards C ... 
 travels straight on. 
C 
F' 
F 
Rule 3 
Construction rules for concave lenses 
3	 Graphical construction of image formation 
b	Drawing ray diagram 
convex lens 
concave lens 
Click the following to see how to draw ray diagrams. 
Q1 	 Which of the following... 
Which of the following incident rays is mentioned in the construction rules? 
A 
F 
F’ 
C 
F 
F’ 
B 
F 
F’ 
Q2 	 Which of the following light  
Which of the following light rays is correct ? 
F’ 
F 
A 
B 
C 
Q3 	 How to find the focus of the... 
Step 1: Draw a light ray A parallel to the principal axis from the tip of the arrow. 
O 
I 
Q3 	 How to find the focus of the... 
Step 2: By the construction, the ray A appears to come from the ______ and the extended part ________ the tip of the image. 
O 
I 
focus 
passes 
Q3 	 How to find the focus of the... 
Step 3: The point where the extended refracted light ray A cross the ______________ is the focus. 
O 
I 
principal axis 
F 
 magnification m 
= 
height of image (image size) 
height of object (object size) 
c	Magnification 
3	 Graphical construction of image formation 
F' 
C 
F 
I 
O 
F' 
C 
F 
I 
O 
magnification m = 
 image distance 
object distance 
v 
u 
Also, 
 m = 
v 
u 
3	 Graphical construction of image formation 
Studying images formed by a convex lens 
Video 
4	 Position and nature of image 
Convex lens refracts the rays to form an inverted image on a plane at the principal focus. 
 Such a plane is called the focal plane . 
focal plane 
convex lens 
f 
construction ray 
We can find the position and nature of image by drawing ray diagram 
∴ The 2 parallel rays also converge to I . 
C 
F' 
F 
I 
4	 Position and nature of image 
Images formed by a convex lens 
object : 
image : 
at infinity 
at F , real, inverted and diminished 
C 
2 F' 
F' 
2 F 
F 
I 
object : 
image : 
beyond 2 F ’ 
between F and 2 F 
real, inverted and diminished 
C 
2 F' 
F' 
2 F 
F 
O 
I 
object : 
image : 
at 2 F ’ 
at 2 F 
real, inverted and same size 
C 
2 F' 
F' 
2 F 
F 
O 
I 
object : 
image : 
between F ’ and 2 F ’ 
beyond 2 F 
real, inverted and magnified 
C 
2 F' 
F' 
2 F 
F 
O 
I 
object : 
image : 
at F ’ 
at infinity 
C 
2 F' 
F' 
2 F 
F 
O 
object : 
image : 
< F ’ 
on the same side as the object 
virtual, erect and magnified 
O 
I 
C 
2 F' 
F' 
2 F 
F 
Images formed by a convex lens 
Simulation 
Simulation 
4	 Position and nature of image 
Images formed by a concave lens 
C 
F' 
F 
I 
object : 
image : 
at infinity 
at F’ 
2 F' 
2 F 
C 
F' 
F 
object : 
image : 
within 2 F ’ (or near object) 
between F ’ and 2 F ’, on the same side of object 
2 F' 
2 F 
O 
I 
virtual, erect and diminished 
Images formed by a concave lens 
Simulation 
Simulation 
Example 6 
An object is positioned between F ’ and 2 F ’ of convex lens. 
Complete the rays. 
( a)	Locate the image. 
( b)	Is it a virtual or a real image? 
2 F' 
F’ ’ 
O 
F 
2 F 
Example 6 
( a) 
( b)	It is a real image. 
2 F' 
F 
2 F 
F’ ’ 
O 
I 
Example 7 
An object is positioned between F ’ and 2 F ’ from concave lens. 
Complete the rays. 
( a)	Locate the image. 
( b)	Is it a virtual or a real image? 
2 F' 
F’ ’ 
O 
F 
2 F 
Example 7 
( a) 
( b)	It is a real image. 
2 F' 
F’ ’ 
O 
F 
2 F 
I 
Example 8 
An object of height 5 cm is placed at 15 cm from a convex lens of focal length 10 cm. 
Find the position and magnification of the image. 
C 
F' 
2 F 
F 
O 
5 cm 
5 cm 
C 
F' 
2 F 
F 
O 
5 cm 
5 cm 
height of object 
height of image 
= 10 cm 
= 5 cm 
m 
= 
10 cm 
5 cm 
= 2 
Example 8 
I 
C 
F' 
2 F 
F 
O 
5 cm 
5 cm 
I 
object distance 
image distance 
= 30 cm 
= 15 cm 
m 
= 
30 cm 
15 cm 
= 2 
Alternatively, 
Example 8 
Q1 	 A boy holds a magnifying... 
A boy holds a magnifying glass at arm’s length. 
He looks at a poster through the glass and sees a magnified erect image. 
What happens to the image if he moves the lens closer to his eyes? 
Q1 	 A boy holds a magnifying... 
What happens to the image if he moves the lens closer to his eyes? 
A	It gets larger till it gets totally blurred at some distance. 
B	It gets larger, keeping erect all the way. 
C	It gets smaller and becomes totally blurred at some distance. 
D	It gets smaller, keeping erect all the way. 
Q2 	 If you can capture an image... 
If you can capture an image of a doll on a screen using a lens, 
which of the following may NOT be correct? 
A	The lens you use is a convex lens. 
B	The image is magnified. 
C	The image is real. 
D	The image is erect. 
Q3 	 In the diagram, a ray parallel... 
In the diagram, a ray parallel to the principal axis of the lens is reflected backwards. 
What is the focal length of the cylindrical convex lens? 
A	5 cm 
B	10 cm 
C	20 cm 
D	40 cm 
10 cm 
Q4 	 What happens to the image 
What happens to the image when the plane mirror is moved backwards? 
A	The image becomes blurred. 
B	The image becomes smaller. 
C	The image does not change. 
Q5 	 Both convex and concave... 
Both convex and concave lenses can produce _______ images, which must be _________ than the object if convex lenses are used. 
virtual 
larger