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## Lenses

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Peep-hole.

Watch.

Camera.

Security mirror.

Magnifying glasses.

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?

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

concave lens

(converging lens)

(diverging lens)

1 Convex and concave lenses

a Converging or Diverging?

convex lens

concave lens

(converging lens)

(diverging lens)

1 Convex and concave lenses

a Converging lens

bend the light inwards

You may remember ‘converging’ as ‘concentrating’.

1 Convex and concave lenses

a Diverging lens

bend the light outwards

You may remember ‘diverging’ as ‘dividing’.

1 Convex and concave lenses

a Converging or diverging?

Recall that light travels more slowlyin glass than in air.

Light converges or diverges as some parts of the wavefronts lag behind.

converges

diverges

- Parallel rays are refracted inwards.

principal focus

- Refracted rays meet at a point called the principal focus F.

F

F'

F

- A convex lens has 2 principal foci.

- 1 on each side

C

principal axis

- The line through the optical centre and 2 foci is called the principal axis.

Parallel rays are refracted outwards.

principal focus

- Refracted rays appear to spread from a point called the principal focus F.

F

F'

F

- A concave lens has 2 principal foci.

- 1 on each side

C

principal axis

- The line through the optical centre and 2 foci is called the principal axis.

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?

X

Y

Z

A Path X.

B Path Y.

C Path 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?

X

Y

Z

A Path X.

B Path Y.

C Path Z.

2 Image formation by a lens

O

screen

When the light from a point of an object enters our eyes,

we can see the point.

I

2 Image formation by a lens

I

O

b Virtual images

Light rays diverge from a point.

No rays actually come from the image.

Hence called ‘virtual’.

convex lens

O

screen

Since only convex lensesconverge light rays, real images can only be formed by convex lenses.

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

Rule 1

A ray parallel to the principal axis...

F

C

…is refracted through F.

Construction rules for convex lenses

Rule 2

A ray passing through F'...

F

F'

C

…is refracted parallel to the principal axis.

Construction rules for concave lenses

Rule 1

A ray parallel to the principal axis...

C

F'

F

…is refracted so that it appears to come from F'.

Construction rules for concave lenses

Rule 2

A ray directed towards F...

C

F'

F

…is refracted parallel to the principal axis.

3 Graphical construction of image formation

b Drawing ray diagram

Click the following to see how to draw ray diagrams.

convex lens

concave lens

Q1 Which of the following...

A

B

F

F’

F

F’

C

F

F’

Which of the following incident rays is mentioned in the construction rules?

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.

focus

passes

O

I

Q3 How to find the focus of the...

Step 3: The point where the extended refracted light ray A cross the ______________ is the focus.

principal axis

O

I

F

I

C

F'

O

3 Graphical construction of image formationc Magnification

magnification m

height of image (image size)

=

height of object (object size)

v

F

I

C

F'

O

3 Graphical construction of image formationAlso,

image distance

v

m =

magnification m =

u

object distance

4 Position and nature of image

f

Convex lens refracts the rays to form an inverted image on a plane at the principal focus.

convex lens

focal plane

Such a plane is called the focal plane.

C

F'

F

I

We can find the position and nature of image by drawing ray diagram

∴ The 2 parallel rays also converge toI.

4 Position and nature of image

I

Images formed by a convex lens

F

2F

C

2F'

F'

at infinity

object:

image:

at F , real, inverted and diminished

4 Position and nature of image

I

Images formed by a concave lens

2F

F

C

F'

2F'

object:

at infinity

image:

at F’

I

F

2F

2F'

C

F'

object:

within 2F ’ (or near object)

image:

between F ’ and 2F ’, on the same side of object

virtual, erect and diminished

Example 6

O

2F

F

2F'

F’’

An object is positioned between F’ and 2F’ of convex lens.

Complete the rays.

(a) Locate the image.

(b) Is it a virtual or a real image?

Example 7

O

An object is positioned between F ’ and 2F ’ from concave lens.

Complete the rays.

F’’

F

2F

2F'

(a) Locate the image.

(b) Is it a virtual or a real image?

Example 8

O

F

2F

F'

C

5 cm

5 cm

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.

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...

10 cm

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

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.

larger

virtual

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