1. Convex and Concave Lenses
Refracting Light Through Transparent Media
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2. Types of Lenses Lenses are used in our everyday lives
They are in microscopes, telescopes, binolculars, cameras (even the ones in cell phones)
A lens is a curved transparent material that is smooth and regularly shaped so that when light strikes it, the light refracts in a predictable and useful way

3. Types of Lenses (cont’d)
There are two types of lenses you will examine in this lesson
Convex or Converging Lenses: light rays are focussed through a focal point
Concave or Diverging Lenses: light rays are spread out from a focal point
The following diagrams will demonstrate these properties

4. Types of Lenses (cont’d)
focal point, F
focal point, F'
convex lens
(side profile)
focal point, F’
focal point, F
concave lens
(side profile)

5. Lens Terminology
Similar to mirrors, there is a principal axis that is an imaginary horizontal line drawn through the optical centre of the lens
The axis of symmetry is an imaginary vertical line drawn through the optical centre of the lens
The exact centre of the lens is called the optical centre

6. Lens Terminology (cont’d)
axis
of symmetry
principal
axis
optical
centre
convex lens
(side profile)
axis
of symmetry
principal
axis
optical
centre
concave lens
(side profile)

7. Lens Terminology (cont’d)
There are 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
On the opposite side is the focal point on the other side of the lens is given the symbol F′
The following slide illustrates this more clearly

8. Lens Terminology (cont’d)
focal point, F
Focal points on the opposite side are called, F’
focal point, F'
Rays go through focal point, F.
convex lens
(side profile)
Rays appear to be coming from focal point, F.
Focal points on the opposite side are called, F’
focal point, F’
focal point, F
concave lens
(side profile)

9. Lens Terminology (cont’d)
The focal length, f, is the distance from the axis of symmetry to the principal focus
Since the light behaves the same way travelling in either direction through the lens, both types of thin lenses have two equal focal lengths.

10. Lens Terminology (cont’d)f f
principal
axis
focal point, F
focal point, F'
convex lens
(side profile) f f
principal
axis
focal point, F
focal point, F’
concave lens
(side profile)

11. Concave or Diverging Lenses
A diverging or concave lens refracts light away from the principal axis of the lens.
This means that light rays will never cross once they have passed through the lens.
The image formed is always upright and smaller than the object.
The reasons for this will be illustrated in the next few slides that describe how to draw ray diagrams for concave lenses.
The image formed is a virtual image.

12. Ray Diagrams for Concave or Diverging Lenses
Notice how the image that is formed is smaller and a virtual image
2. The first ray continues on an angle that is in line with the focal point, F.
1. The first ray is drawn from the object to the axis of symmetry
3. A dotted line is used to show the continuation of the refracted ray back to the focal point.
principal
axis
object
virtual
image F F’
If someone looked through the lens they would see the arrow on the other side, right side up and smaller.
4. A second ray is drawn from the object through the optical centre of the lens.
5. Where the dotted line and the second ray intersect is the position of the virtual image.
concave lens
(side profile)

13. Ray Diagrams for Concave or Diverging Lenses (cont’d)
Go to and login
Go to the “Ray Tracing (Lenses)” Gizmo to see how moving the object closer to the focal point makes it bigger.
Choose concave lens in the lens options
Move around the focal point to observe what happens to the lens and the image that is formed.
Notice how they use three rays instead of two

14. Convex or Converging Lenses
A convex or converging lens refracts light towards the principal axis.
This means that all light rays focus though a single focal point.
Images formed by a convex lens depend on where the object sits relative to the focal point, F’.
Convex lenses can form both real and virtual images
The following slides will illustrate how to draw ray diagrams for convex lenses.

15. Ray Diagrams for Concave or Converging Lenses
Notice how the image that is inverted and a real image
2. The first ray continues on an angle that runs through the focal point, F.
1. The first ray is drawn from the object to the axis of symmetry.
5. Where the two rays cross is the location of the image.
real
image
principal
axis
object F F’
3. A second ray is drawn from the object through the focal point, F’ to the axis of symmetry.
4. The second ray continues on, parallel to the principal axis
concave lens
(side profile)

16. Ray Diagrams for Concave or Converging Lenses (cont’d)
Let’s look at what happens if the object is closer to the focal point, F’
2. The first ray continues on an angle that runs through the focal point, F.
1. The first ray is drawn from the object to the axis of symmetry.
Compared with the previous example, the real image formed is much larger.
5. Where the two rays cross is the location of the image.
real
image
principal
axis
object F F’
3. A second ray is drawn from the object through the focal point, F’ to the axis of symmetry.
4. The second ray continues on, parallel to the principal axis
concave lens
(side profile)

17. Ray Diagrams for Concave or Converging Lenses (cont’d)
5. A dotted line is drawn back from the intersection between the second ray the axis of symmetry
4. A second ray is drawn from the object to the axis of symmetry in line with the focal point, F’. The line is refracted parallel to the principal axis
Let’s look at what happens if the object is closer to the lens than focal point, F’.
1. The first ray is drawn from the object to the axis of symmetry.
3. A dotted line is drawn back from the first ray.
virtual
image
principal
axis
object F F’
6. Where the two dotted line cross, is where the virtual image is formed.
If someone looked through the lens they would see the arrow on the other side, right side up and larger.
2. The first ray continues on an angle that runs through the focal point, F.
Notice that the image formed is upright and a virtual image.
concave lens
(side profile)

18. Ray Diagrams for Concave or Diverging Lenses (cont’d)
Go to and login
Go to the “Ray Tracing (Lenses)” Gizmo to see how moving the object closer to the focal point makes it bigger.
Choose convex lens in the lens options
Move around the focal point to observe what happens to the lens and the image that is formed.
Notice how they use three rays instead of two

19. Thin Lens Equation
The distance of the object from the lens, do, the distance of the image from the lens, di, and the focal length of a lens, f, can all be related using the Thin Lens Equation.
Go to page 455 – 457 of the textbook to see examples of calculations involving the thin lens equation.

20. Draw Ray Diagrams
Go to the word document for this lesson and print out the ray diagram pages.
Complete the ray diagrams for the concave and convex lenses.
You only need to do rays for the tip of the arrow, just like you learned in the previous slides.

21. Quick Lab Go to page 459 and perform the Quick Lab
Read the instructions carefully.
Answer questions 10 and 11.

22. Questions from the Textbook
Answer Questions 1, 2, 5, 6, 8 and 10 on page 462 of the textbook.