1. Part 3: Optics (Lenses and Mirrors)
LIGHT
Part 3: Optics (Lenses and Mirrors)

2. Key Terms Convex: converging; has a surface that bulges outward
Concave: diverging; has a surface that bulges inward
Focal point: the point on the axis of a lens or mirror to which parallel rays of light converge
Center of curvature: length
equivalent to the radius
of the mirror/lens
Vertex: center of the curve
of the mirror
Principle Axis: line that passes through the center of the lens, perpendicular to the lens surface

3. Images can be….
Image: a picture or appearance of a real object formed by light that is reflected or refracted and can be categorized as either real or virtual
Inverted: upside-down from the original object (
Up-Right: The same orientation as the original object
Real image: image formed by diverging light rays; has a positive image distance (will be upside down)
Virtual image: image formed by converging light rays; has a negative image distance (will be up-right)
Larger or smaller than original object

4. 1/do + 1/di = 1/f Lens and Mirror Equation do = object distance
f = focal length (distance from the focal point to the center of the lens)
positive for concave mirrors
negative for convex mirrors
do = object distance
usually positive
di = image distance
can be + or –

5. Mirrors

6. Flat Mirror Images 1. virtual 2. upright 3. same size as object
Images formed by flat mirrors are always:
1. virtual
(virtual images are always behind mirrors)
2. upright
(virtual images are always upright)
3. same size as object
(if the image is larger or smaller, the mirror isn’t flat)
4. Left and right are reversed
5. located as far behind the mirror
as the object is in front

8. To see your full body in a mirror, how tall MUST the mirror be?

9. Plane Mirror
You only need a mirror ½ your height to see your whole body!!
This is because of the law of reflection

10. LENSES

11. Note: Light always bends toward thickest part of lens
transparent material that refracts light to form an image
Focal Length
Converging Lens
Diverging Lens F F f
Focal Point f
(Convex)
(Concave)
Note: Light always bends toward thickest part of lens

12. Real Image formed by actual convergence of light rays Usually inverted
Converging Lens F f
(Convex)

13. Virtual Image formed by apparent convergence of light rays
Usually right-side-up
Diverging Lens F f
(Concave)

14. Diverging Lens (Double Concave)
Diverging Lens spread the light waves apart from each other
Virtual focus
Focus = -
Can form only virtual,
upright and smaller
images

15. Enlarged virtual images
Converging Lens
(Double Convex)
Converging Lens bring the light waves together to meet at a single point
Principle
focus
Parallel rays
Focus = +
Can form real images
(enlarged or reduced
& inverted) or
Enlarged virtual images

16. Rays Diagrams for Converging Lens
(Double Convex)
A ray thru the
Center of the
lenses
Parallel ray
Passes thru
The focus
focus (f)
2 f x
Remains
unbent
Focal ray
Refracts parallel
To principal axis

17. Light passes through a lens
Ray Tracing for Lenses
Light passes through a lens
There is a focal point on both sides of a lens
Ray #1: Parallel to the axis Refracts through F
Converging Lens:
Ray #2: Through F Refracts parallel to axis
Ray #3: Through Center of lens undeflected

18. Object Beyond 2f Converging Lens
Image is:
Real
Inverted
Reduced
Appears between
f and 2f
Parallel ray
focus (f)
2 f x
Focal ray
Object beyond 2f

19. Example: Camera

20. Object at 2f Converging Lens
Image is:
Real
Inverted
Same size
Appears between
f and 2f
Parallel ray
focus (f)
2 f x
Focal ray
Object at 2f

21. Object Between 2f & f Converging Lens
Image is:
Real
Inverted
Enlarged
Appears beyond 2f
Parallel ray
focus (f)
2 f x
Focal ray
Object between
f and 2f

22. Example: Slide Projector

23. Object Between f &Converging Lens
Image is:
Virtual
Erect
Enlarged
Appears on same
Side as Object
Apparent
Convergence
Of rays
focus (f)
2 f x
Object
Inside
focus

24. * Convergent lenses can produce real or virtual images
Example: Magnifying Glass
Web Link: Ray tracing

25. Object at f
Image is:
Not formed
focus (f)
2 f x
Object at the
focus

26. In summary:
If an object is at the focal point, there is not image formed.
If an object is between the focal point and the lens, the image is virtual.
If an object is beyond that focal point, the image is real.

27. 1/do + 1/di = 1/f Reminder: Lens and Mirror Equation
f = focal length (distance from the focal point to the center of the lens)
positive for convex lenses
negative for concave lenses
do = object distance
usually positive
di = image distance
can be + or –

28. Sign conventions for Lenses
Focal length (f)
+ converging
- diverging
Object distance (do)
+ object on the left
Image distance (di)
+ image on the right (real)
- image on the left (virtual)

29. An object is placed 3 m from a convex lens with a focal length of 10 cm. How far from the lens does the image appear?
10 cm
3 m
(not to scale)

30. = 0.103 m di Find LCD 1 = + f do di = 29 3 di 1 1 = + 0.1 3 di = 3 29
An object is placed 3 m from a convex lens with a focal length of 10 cm. How far from the lens does the image appear?
10 cm
3 m 1 = + f do di = 29 3 di 1 1 = +
0.1 3 di = 3 29 di 1 di = ? = - 1
0.1 3 di
Find LCD do =
3 m f =
10 cm = 0.1 m = - 30 3 1 di =
0.103 m di

31. An object is placed 4 cm from a convex lens with a focal length of 10 cm. How far from the lens does the image appear?
4 cm
10 cm

32. = -6.67 cm di on same side as object! Find LCD 1 = + f do di = -3 20
An object is placed 4 cm from a convex lens with a focal length of 10 cm. How far from the lens does the image appear?
10 cm
4 cm 1 = + f do di = -3 20 di 1 1 = + 10 4 di di = ? = 20 -3 di 1 do =
4 cm = - 1 10 4 di
on same side as object!
Find LCD f =
10 cm =
-6.67 cm di = - 2 20 5 di 1