Images in Lenses

ConvergingDiverging

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Lens

• A transparent material that is has at least one curved side

• Refracts light in a predictable and useful way

Types of Lenses

Converging Lens• makes parallel light rays

come together • Also known as convex

lens• Thicker at the center,

thinner at the edges

Types of Lenses

Diverging Lens• makes parallel light rays

move apart• Also known as concave

lens• Thinner in the center,

thicker at the edges

Lens Function• Change the appearance of

objects (image appears larger, smaller, upside down or misshapen)

• Magnify images

• Project images onto a screen

Terminology• Optical Centre (O) – centre of the lens; also the

point where the principal axis crosses• Axis of Symmetry – an imaginary vertical line

drawn through the optical center of a lens; perpendicular to principal axis

Optical Centre (O)

Focal Point

• Since lenses have 2 sides, they have a focal point on each side.

• The principal focus is where the light rays converge• A converging and diverging mirror has the principal

focus on different sides of the lens

Focal Point – Converging Lens

• Principal focus is on the opposite side of the lens as the incident rays

Principal FocusSecondary Principal Focus

Focal Point – Diverging Lens

• Principal focus is on the same side of the lens as the incident rays

• The focal point is virtual

Focal Length

• Focal length (f) is the distance between the principal focus and optical centre

• Distance from F to O, F to 2F, F’ to O, F’ to 2F are all equal.

• 2F and 2F’ are twice the distance away from the optical centre than the focus points.

FF’ 2F2F’ O

TerminologyPrincipal Focus (F)• A point on the principal axis where the light rays that are traveling

parallel to the principal axis appear to converge• In a converging lens it is on the opposite side as the incident rays• In a diverging lens it on the same side as the incident rays

Secondary Principal Focus (F’)• Focus that is on the opposite side as the principal focus, located the

same distance from the lens as F• In a converging lens it is on the same side as the incident rays• In a diverging lens it is on the opposite side as the incident rays

Focal Length (f)• distance from the principal focus to the axis of symmetry• Focal length is the same distance with the secondary principal focus

Light Rays with a Converging Lens

1. A light ray parallel to the principal axis will refract through the principal focus (F).

2. A light ray passing through the secondary principal focus (F’) will refract parallel to the principal axis.

3. A light ray through the optical centre (O) will keep travelling in the same direction without being refracted.

Light Rays with a Converging Lens

1. A light ray parallel to the principal axis will refract through the principal focus (F).

Light Rays with a Converging Lens

1. A light ray parallel to the principal axis will refract through the principal focus (F).

FF’

LOCATING AN IMAGE ON A CONVERGING LENS

2F’ 2F’

2F’ 2F’

2F’2F’

2F’2F’

Light Rays with a Converging Lens

1. A light ray parallel to the principal axis will refract through the principal focus (F).

2. A light ray passing through the secondary principal focus (F’) will refract parallel to the principal axis.

Light Rays with a Converging Lens

2. A light ray passing through the secondary principal focus (F’) will refract parallel to the principal axis.

FF’

LOCATING AN IMAGE ON A CONVERGING LENS

2F’ 2F’

2F’ 2F’

2F’2F’

2F’2F’

Light Rays with a Converging Lens

1. A light ray parallel to the principal axis will refract through the principal focus (F).

2. A light ray passing through the secondary principal focus (F’) will refract parallel to the principal axis.

3. A light ray through the optical centre (O) will keep travelling in the same direction without being refracted.

Light Rays with a Converging Lens

3. A light ray through the optical centre (O) will keep travelling in the same direction without being refracted.

FF’

LOCATING AN IMAGE ON A CONVERGING LENS

2F’ 2F’

2F’ 2F’

2F’2F’

2F’2F’

LOCATING AN IMAGE ON A CONVERGING LENS

• What happens when object is at F’?

2F’ 2F’

LOCATING AN IMAGE ON A CONVERGING LENS

1. Pick a point on the object (usually the top of the object)

2. Send any two light rays off the point on the object.

3. Determine the refracted rays. Light rays only refract when it hits the lens

4. Find the intersection of the light rays. If the rays do not intersection, extend the refracted ray until they do (exception: don’t do this for parallel light rays)

5. Use the point of intersection to location off an object is needed to locate its image.

LOCATING AN IMAGE ON A CONVERGING LENS

Ray 1 – travels parallel to the principal axis and is refracted through the principal focus (F)

LOCATING AN IMAGE ON A CONVERGING LENS

Ray 2 – travels through the optical centre (O) and continues straight without being refracted

LOCATING AN IMAGE ON A CONVERGING LENS

Ray 3 (optional since you only need 2 lines to form an intersection) – travels through the secondary principal focus (F’) and refracts parallel to the principal axis

LOCATING AN IMAGE ON A CONVERGING LENS

Draw the image given the point of intersection.

LOCATING AN IMAGE ON A CONVERGING LENS

5 Scenarios for the Object1. Beyond 2F’: Object is greater than 2 focal

lengths from the lens (do>2f)2. At 2F’: Object is at 2 focal lengths (do=2f)3. Between 2F’ and F’: Object is between 1 and

2 focal lengths from the lens (f<do<2f)4. At F’: Object is at the focal point (do=f)5. Between F’ and lens: Object is less than 1

focal length away from the lens (0<do<f)

Case 1 – Object beyond 2F’

Size Attitude Location Type

Reduced Inverted Between F and 2F Real

Converging LensObject beyond 2F’

Case 2 – Object at 2F’

Size Attitude Location Type

Same size Inverted At 2F Real

Size Attitude Location Type

Case 3 – Object between 2F’ and F’

Enlarged

Inverted Beyond 2F Real

Size Attitude Location Type

Case 4 – Object at F’

No Image Formed!

Size Attitude Location Type

Case 5 – Object between F’ and lens

Enlarged

Upright Same side as object

Virtual

Converging LensObject between F’ and Lens

CONVERGING LENSESThe first lens known to be used was a converging lens called a reading stone. Reading stones formed images that were upright and larger than the object.

How can a converging lens produce both upright and inverted images?

DIVERGING LENSES

DIVERGING LENSES

• The focal point is virtual• Thus the principal focus is on the same side

of the lens as the incident rays

DIVERGING LENSES

Light Rays with a Diverging Lens

1. A light ray parallel to the principal axis will refract through the principal focus (F).

2. A light ray passing through the secondary principal focus (F’) will refract parallel to the principal axis.

3. A light ray through the optical centre (O) will keep travelling in the same direction without being refracted.

Light Rays with a Diverging Lens

1. A light ray parallel to the principal axis will refract through the principal focus (F).

F’F 2F’2F O

Light Rays with a Diverging Lens

2. A light ray passing through the secondary principal focus (F’) will refract parallel to the principal axis.

F’F 2F’2F O

Light Rays with a Diverging Lens

3. A light ray through the optical centre (O) will keep travelling in the same direction without being refracted.

F’F 2F’2F O

LOCATING AN IMAGE ON A DIVERGING LENS

1. Pick a point on the object (usually the top of the object)

2. Send any two light rays off the point on the object.

3. Determine the refracted rays. Light rays only refract when it hits the lens

4. Find the intersection of the light rays. If the rays do not intersection, extend the refracted ray until they do (exception: don’t do this for parallel light rays)

5. Use the point of intersection to location off an object is needed to locate its image.

LOCATING AN IMAGE ON A DIVERGING LENS

• Q. Draw the ray diagram for this pencil to locate its image

F’F 2F’2F O

LOCATING AN IMAGE ON A DIVERGING LENS

F’F 2F’2F O

Ray 1 – travels parallel to the principal axis and is refracted through the principal focus (F)

LOCATING AN IMAGE ON A DIVERGING LENS

F’F 2F’2F O

Ray 2 – travels through the secondary principal focus (F’) and refracts parallel to the principal axis

LOCATING AN IMAGE ON A DIVERGING LENS

F’F 2F’2F O

Ray 3 (optional since you only need 2 lines to form an intersection)

travels through the optical centre (O) and continues straight without being refracted

LOCATING AN IMAGE ON A DIVERGING LENS

F’F 2F’2F O

Size Attitude Location Type

Reduced Upright Same side as object

Virtual

Diverging Lens

The image formed is always virtual, upright and smaller

Concave Lens Ray Diagrams

Ray 1 - travels from the tip of the object parallel to the principal axis. When it emerges from the lens, it appears to come from the principal focus (F)

Concave Lens Ray Diagrams

Ray 2 - travels from the tip of the object through the optical centre of the lens and is not refracted.

Concave Lens Ray Diagrams

The image occurs where these rays appear to intersect.