Images Formed By Lenses

Section 12.2Pages 494 - 498

Lens Terminology

The principal axis is an imaginary line drawn through the optical centre perpendicular to both surfaces.

The axis of symmetry is an imaginary vertical line drawn through the optical centre of a lens.

Lens TerminologyBoth types of lenses

have two principal focuses.

The focal point where the light either comes to a focus or appears to diverge from a focus is given the symbol F, while that on the opposite side of the lens is represented by Fʹ.

Lens Terminology

The focal length, f, is the distance from the axis of symmetry to the principal focus measured along the principal axis.

Both types of thin lenses have two equal focal lengths.

Drawing a Ray Diagram for a LensThe light rays will bend, or refract, away from the lens

surface and toward the normal. When the light passes out of the lens at an angle, the

light rays refract again, this time bending away from the normal.

The light rays undergo two refractions:1st on entering the lens2nd on leaving the lens.

When Drawing Ray Diagrams for a Lens ... Keep in mind ...A thin lens is a lens that has a thickness that is slight

compared to its focal length. An example of a thin lens is an eyeglass lens.

You can simplify drawing a ray diagram of a thin lens without affecting its accuracy by assuming that all the refraction takes place at the axis of symmetry.

DIVERGING LENSESA diverging lens is sometimes called a

concave lens because it is thinner in the centre than at the edges.

As parallel light rays pass through a concave lens, they are refracted away from the principal axis.

The light rays spread apart (diverge) and they will never meet on the other side of the lens.

You may remember “diverging” as “dividing”.

PROPERTIES OF DIVERGING LENSESRefracted rays appear to spread from a virtual focus called the

principal focus, F.It is on the same side as the incident rays.The secondary principal focus, F’, is located on the other side of

the lens. Focal length (f), optical centre (O), and principal axis are the same

as in a converging lens.

Principal axisF’

Principal focus

O

Focal length (f)

Locating Images in Diverging Lens

The image rules for diverging lenses are similar to those for a converging lens. The only difference is that light rays do not actually come from the principal focus (F); they only appear to.

Follow along with Table 12.2 on page 497 of the textbook.

Locating Images in Diverging Lenses

Any two of the following rays may be used to locate the image:

1. Draw a ray parallel to the principal axis that is refracted through the principal focus (F).

2. Draw a ray that passes through the secondary principal focus (F') and refracts parallel to the principal axis.

3. A ray that passes through the optical center goes straight through, without bending.

Only two of these lines are needed to find the image.

Drawing a Diverging Lens Ray Diagram

S: Smaller A: Upright L: Between F and axis of symmetry

T: Virtual

2F F F’’ 2F’

Ray Diagrams - Diverging LensesDiverging lenses always produce the same images.

Smaller, upright, virtual, and on the same side of the lens as the object.

As the object moves farther from the lens, the image becomes smaller.

CONVERGING LENSESA converging lens is also called a

convex lens because it is thicker at the centre than at the edges.

All incident parallel light rays converge at a single point after refraction.

You may remember “converging” as “concentrating”.

Converging lenses are often used as magnifying glasses.

PROPERTIES OF CONVERGING LENSESCentre of the lens is called the optical centre, O.Refracted rays meet at a point called the principal focus, F.It is located on the opposite side of the incident rays.Light can strike the lens from either side, and both sides can focus

parallel rays. Thus, there can be a secondary principal focus, F’, on the same side as the incident rays.

Principal axisF’

Principal focus

O

Focal length (f)

PROPERTIES OF CONVERGING LENSESBoth F and F’ are equal distance from the optical centre.The line through the optical centre and the two foci is

called the principal axis.The distance between F to O is the focal length, f, of the

lens.

Principal axisF’

Principal focus

O

Focal length (f)

PROPERTIES OF CONVERGING LENSESLight can strike the lens from either side and both sides

can focus parallel rays.Thus, there can be a secondary principal focus, F’, on

the same side as the incident rays.Both F and F’ are equal distance from the optical centre.

Principal axisF’

Principal focus

O

Focal length (f)

Drawing a Converging Lens Ray Diagram1. Any ray parallel to the principal axis is refracted

through the principal focus (F).2. A ray that passes through the secondary principal

focus (F') is refracted parallel to the principal axis.3. A ray that passes through the optical center goes

straight through, without being refracted (bending).

As with converging mirrors, only two rays are required to locate an image. The third one acts as a check.

OBJECT IMAGE CHARACTERISTICSLOCATION SIZE

(smaller, larger, or same)ATTITUDE(inverted or upright)

LOCATION TYPE(Real or virtual)

Beyond 2F’

At 2F’

Between 2F’ and F’At F’

Between F’ and mirror

SUMMARY: IMAGING PROPERTIESOF A CONVERGING LENS

JIGSAWThere are 5 scenarios to investigate with CONVERGING

LENS.You will be placed in groups and assigned a scenario to

work on, during which time you will become the ‘expert’ on that scenario.

Afterwards, everyone will JIGSAW into another group where you will all have a turn to ‘teach’ your new group members about your converging lens scenario.

Please reference your textbook (p.495) during this activity.

JIGSAW GROUPSGROUP 1 GROUP 2 GROUP 3 GROUP 4 GROUP 5Adoma Julia Akin Haya

AngelicaAnnamaria Anthony Victor Andre AlexHelder Stephanie Michael Ivo

CristianVanessa Jonathan Alissia Josie GabrielDavid Abdullah Higor Matthew SevakStephen Raffaela Rachel Victoria

OBJECT IMAGE CHARACTERISTICSLOCATION SIZE

(smaller, larger, or same)ATTITUDE(inverted or upright)

LOCATION TYPE(Real or virtual)

Beyond 2F’

At 2F’

Between 2F’ and F’At F’

Between F’ and mirror

SUMMARY: IMAGING PROPERTIESOF A CONVERGING LENS

OBJECT IMAGE CHARACTERISTICSLOCATION SIZE

(smaller, larger, or same)ATTITUDE(inverted or upright)

LOCATION TYPE(Real or virtual)

Beyond 2F’ Smaller Inverted Between F and 2F

Real

At 2F’ Same size Inverted At 2F Real

Between 2F’ and F’

Larger Inverted Beyond 2F Real

At F’ NO CLEAR IMAGE FORMED(Emergent rays are parallel)

Between F’ and mirror

Larger Upright Virtual

SUMMARY: IMAGING PROPERTIESOF A CONVERGING LENS

Solutions for JIGSAW Diagrams

Object between 2F’ and F’

S: Larger A: Inverted L: Beyond 2F T: Real

2F’ F’ F 2F

Object beyond 2F’ (An object more than two times the distance of the focal length from the lens)

2F’ F’ F 2F

S: Smaller A: Inverted L: Between F and 2F

T: Real

Object at 2F’

S: Same size A: Inverted L: At 2F T: Real

2F’ F’ F 2F

Object at F’

NO IMAGE FORMED

2F’ F’ F 2F

Object in front of F’

2F’ F’ F 2F

S: Larger A: Upright L: Behind F’ T: Virtual

Solutions for Converging Lens