5.4 Lenses

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Understanding Lenses Understanding Lenses

Transcript of 5.4 Lenses

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Understanding LensesUnderstanding Lenses

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Lenses are made of __________ material such as glass or clear plastics.

They have two faces, of which at least one is ______

Understanding LensesUnderstanding Lenses

transparent

curved

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Types of lenses:

(a) ______ lens, also known as

converging lens. It is ________ at

the centre of the lens.

Biconvex Plano convex Converging meniscus

Convex

thicker

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(b) ________ lens, also known as

diverging lens. It is _________ at

the centre of the lens.

Biconcave Plano concave Diverging meniscus

Concave

thinner

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Focal Point and Focal Length of a lensFocal Point and Focal Length of a lens(convex lens)(convex lens)

1. When light rays which are parallel and close to the principal axis strikes on a convex lens, they are refracted ________ and converge to a point, F on the principal axis. This point is a _____ _______ of the convex lens.

inwards focal point

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Focal Point and Focal Length of a lensFocal Point and Focal Length of a lens(concave lens)(concave lens)

2. When light rays are parallel to the principal axis fall on a concave lens, they are refracted ___________ and appear to diverge from the focal point, F, on the principal axis.

outwards

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3. The focal point, F is a point on the principal axis where all rays are close and parallel to the axis that _________ to it after passing through a convex lens, or appear to ________ from it after passing through a concave lens.

4. The focal length, f is the distance between the focal point and the ____________________.

5. The optical centre, C is the geometric centre of the lens. It is the point through which light rays pass through without __________.

6. The principal axis is the line passing through C and is _____________ to the lens.

ff

F

ff

F

converge diverge

optical centre

deviation

perpendicular

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)(

1

meterf

The power of lens is related to its focal length by the expression:

Power of lens = Diopter

Power for ___________ lens is positive, and power for _________ lens is negative.

The power of the lens is equal to the reciprocal of its focal length in metres.

convex

concave

)(

1

meterf

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Example 1:

)(

1

meterf

The focal length of a concave lens is given as 30 cm. What is the power of the lens?

Solution:

Power of lens =

3.0

1

=

= -3.33 D

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Example 2:

The power of a lens is labeled as -10D. Name the type of the lens and determine the focal length of the lens.

Solution:

Type of lens: Concave

Focal length =

10

1

Power

1

= = -0.1 m = - 10 cm

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Complete the table below.

Power of the lens/ D Focal length/ cm

+20

-15

-5

+20

5

- 6.67

5

- 20

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Images Formed by LensesConstruction rules for image formed by Convex Lens

Rule 1: A ray parallel to the principal axis is refracted through the focal point, F

Rule 2: A ray passing through the focal point is refracted parallel to the principal axis.

Rule 3: A ray passing through the optical centre, C travels straight without bending.

The point of intersection is the position of the image.The images formed by a convex lens depend on the object distance, u.

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Construction rules for image formed by Concave Lens

Rule 1: A ray parallel to the principal axis is refracted as if it appears coming from the focal point, F which is located at the same side of the incident ray.

Rule 2: A ray passing through the focal point is refracted parallel to the principal axis.

Rule 3: A ray passing through the optical centre, C travels straight without bending.

The point of intersection is the position of the image.The images formed by a concave lens are always virtual, upright and diminished.

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A ______ image can be captured on a screen. A ______ image cannot be captured on a screen

real

virtual

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Magnification, m

The size of an image formed by lens varies with the position of the object.

The linear magnification, m is defined as:

Size of image, hi

Size of object, ho

=Image distance, v

Object distance, u

m = o

i

h

h=u

v

The image is __________ if m > 1The image is __________ if m < 1The image is ______________________ if m = 1

magnified diminished the same as the object

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Characteristic of image formed by a convex lens

Object at infinity (u = )

2F F

F

Characteristics of image:

- Real

- Inverted

- Diminished

- Position of image:

At F (v = f)

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Characteristic of image formed by a convex lens

Object beyond 2F(u > 2f)

2F F

F 2F

Characteristics of image:

- Real

- Inverted

- Diminished

- Position of image: Between F and 2F ( f < v < 2f)

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Characteristic of image formed by a convex lens

Object at 2F(u = 2f)

F F

2F

2F

Characteristics of image:

- Real

- Inverted

- same size as the object (m=1)

Position of image:

At 2F ( v = 2f)

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Characteristic of image formed by a convex lens

Object between F and 2F(f < u < 2f)

2F F F 2F

Characteristics of image:

- Real

- Inverted

- Magnified (m > 1)

Position of image:

Image beyond 2 F

( v > 2f)

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Characteristic of image formed by a convex lens

F F

Characteristics of image:

- Cannot be determined

Position of image:Image at infinity.

Object at F(u = f )

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Characteristic of image formed by a convex lens

Object Between F and C( u < f )

F C F

Characteristics of image:

- virtual

- erect/ Upright

- magnified

Image on the same side of the object.

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Characteristic of image formed by a concave lens

Object beyond 2F(u > 2f)

Characteristics of image:

- virtual

- erect

- diminished

Image on the same side of the object.

F2F F

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Characteristic of image formed by a concave lens

Object between F and C( u < f )

Characteristics of image:

- virtual

- erect

- diminished

Image on the same side of the object.

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Example 1:

An object of 1 cm height is placed 30 cm in front of a convex lens. When a screen is placed at 60 cm at the opposite side of the lens, a sharp image is formed on it.(a) Draw a ray diagram to show the positions of the object and the image. Use a scale of 1 cm to represent 10 cm in the horizontal axis.(b) Find the focal length of the convex lens.(c) Calculate the linear magnification of the image.

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Example 2:

An object of 2 cm height is placed 60 cm in front of a concave lens of focal length 40 cm. (a) Draw a ray diagram to locate the image. Use a scale of 1 cm to represent 10 cm in the horizontal axis. (b) Find the image distance and the magnification.

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Relationship between u, v and f

The image distance, v changes with the object distance, u.How is the focal length of a lens related to the object distance, u and the image distance, v ? Carry out Hands-on Activity 5.9 on page 105 of the practical book.

Carry out Hands-on Activity 5.9 on page 105 of the practical book.

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Lens Formula

The relationship between object distance, u image distance, v andfocal length, f is given by the lens formula:

vuf

111

The lens formula may applied to convex lens and concave lens, provided that the ‘real is positive’ convention sign is followed.

Summary of the significance of the sign for the values of object distance, u, image distance, v and focal length, f is shown in the table below:

Sign Positive value(+) Negative value(-)

u Real Virtual

v Real Virtual

f Convex lens Concave lens

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Problem solving involving lenses

Example 1:An object is placed 15 cm in front of a convex lens of focal length 10 cm. Calculate the image (a) distance, (b) the magnification.

Solution:

(a) Using vuf

111

Image distance, v = 30 cm

m = u

v=

v

1

15

1

10

1

15

30(b)

= 2

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Example 2:An object is placed 20 cm from a concave lens of focal length -15cm.(a) Calculate the image distance.(b) State the characteristics of the image formed.

Solution:

(a) Using vuf

111

v

1

20

1

15

1

Image distance, v = - 8.6 cm

(b) Virtual, upright, diminished

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More exercises:

1. An object is placed in front of a convex lens with focal length of 10 cm. Find the characteristics, position and magnification of the image formed when the object distance is 15 cm.

Answer: The image is real and inverted. Position: v = 30 cm m = 2 times

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2. An object of height 6 cm is placed at a distance of 20 cm from a concave lens of focal length 10 cm. Calculate the position and size of the image. State the characteristics of the image formed.

Answer: v = -6.7 cm Size = 2 cm Characteristics: Virtual, upright, diminished.

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3. A convex lens with focal length of 15 cm formed an image which is real, inverted and same size with the object. What is the object distance from the lens?

Answer: u = 30 cm

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The Uses of Lenses in Optical Devices

Magnifying glass/ Simple microscope

1. It consists of a single ______ lens of ______

focal length.

2. An object is placed at a position _____ _____ the focal length of the lens.

3. The image formed is _____________, _________ and ____________

4. The magnifying power _________ if the focal length of the lens is shorter.

5. A sharper and larger image is seen at the near point of the eye. In general, the near point is taken as 25 cm.

convex short

less than

magnified upright virtual

increases

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Compound Microscope

1. It consists of two powerful _______ lenses of short focal lengths ( 5.0 cm – 10.0 cm)

2. The lens which receives light rays from the object is called the _________ lens. The lens which is used for viewing the final image is called the __________ lens.

3. The focal length of the objective lens is fo

whereas the focal length of the eyepiece lens is fe.

4. The object is placed at a distance between _________________ so that the image formed is _______, ________ and ____ in front of the eyepiece lens.

5. The position of the eyepiece lens is adjusted until the position of the first image is ____ _____ fe from the eyepiece lens

6. The final image formed is ________, _________ and ________

convex

objective

eyepiece

fo and 2fo inverted magnified real

less than

inverted magnified virtual

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Astronomical Telescope1. It consists of an _________ lens and an

__________ lens.

2. The objective lens is used to receive

light rays from distant object.

3. The first image formed is at the focal point of the objective lens Fo. It is _____, ________ and __________

4. The first image now becomes the object

for the eyepiece lens 5. The __________ lens is adjusted so that the first image is situated at the focal point of the eyepiece lens, Fe.

6. The final image formed is at _______. The telescope is said to be in normal adjustment.

7. For normal adjustment of the telescope, the separation between the two lenses is

fo + fe.8. The magnification of the telescope is given by: m =

e

o

f

f

Objective lens Eyepiece lens

objective

eyepiece

real inverted diminished

eyepiece

infinity

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Slide Projector

1. It uses a ______ lens to form a ____, ______ and magnified image of the slide or film on a screen.

2. The slide, being the _____, is placed between ________ from the projector lens

3. The lamp is placed at the focal point of the ________ mirror to reflect all light from the lamp back to the _________

4. The movable projector lens focuses a sharp, _______ and _________ image onto a screen.

5. The slide should be placed upside-down (inverted) in order to form an ________ image on the screen.

Concave mirror Condenser

slideProjector lens Screen

Lamp

image

convex real inverted

object f and 2f

concave condenser

inverted magnified

upright

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Camera

1. The ______ lens is used to produce a ____, _______ and ___________ image on a light sensitive film at the camera.

2. The __________ is used to adjust the size of the aperture, which control the amount of light passing into the camera.

3. The __________ speed is used to control the exposure time when taking photographs.

Focusing screw

Object Convex lens

Diaphragm

Film

shutter

Image

convex real inverted diminished

diaphragm

shutter

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Text book: page 159 Mastery Practice 5.4

Challenge yourself (page 159 and 160)

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