1. Ray Diagrams for Lenses

2. Convex Lens Ray Diagrams
All ray diagrams start with a center line and the lens
Note: the lens can be simplified into a straight vertical line

3. Convex Lens Ray Diagrams
On ray diagrams identify and label the following points:
P – principle axis
C – the optical center
F – real focus (focus on side of lens where light rays emerge)
F’- virtual focus (focus on side of lens where light rays enter)
2F -Twice the real focal length
2F’- Twice the virtual focal length

4. Locate and label the focal points (F) Lenses have 2 focal points
F (real focal point) and F’ (virtual focal point)
The center (C) is located where the lens intersects the center line
Draw the object as described in the problem F’ F C

5. Image Formation
For an image to form multiple rays of light originating from the same point on the object must come together (converge).
To locate the image on a ray diagram, a minimum of 2 rays originating from the same point on object must be shown to meet.
Typically, we represent the forming of an object with three rays called the principle rays.

6. Convex Lens – Principal Rays
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Rays parallel to principal axis are refracted through the real focus (F).
2. Rays through the virtual focus (F’) are refracted parallel to the principal axis.
3. Incident rays along a secondary axis (through O) are not appreciably refracted.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.

7. Ray Diagram: do > 2 f
draw a ray through near F (virtual) to the lens
THEN parallel to the center line (principle axis)
(2) draw a ray parallel to the center line to the lens
THEN through opposite F (real)
(3) draw a ray through C F’ F
The point where the refracted rays intersect is where the image will be formed

8. Ray Diagrams
Sketch a ray diagram for the same height of object but moving closer to 2F.
Do the same but this time your object is between 2F and F.

9. Ray Diagram: 2f > do > f
draw a ray through near F (virtual) to the lens
THEN parallel to the center line (principle axis)
(2) draw a ray parallel to the center line to the lens
THEN through opposite F (real)
(3) draw a ray through C F F

10. Ray Diagram: do < f draw a ray through near F (virtual) to the lens
THEN parallel to the center line (principle axis)
(2) draw a ray parallel to the center line to the lens
THEN through opposite F (real)
(3) draw a ray through C F F
If refracted rays do not meet in “real” space, draw dashed lines back from refracted rays so that they intersect behind the lens

11. What happens when the object is exactly at F? Sketch.
No image formed

12. A convex (converging) lens can form 3 types of images.
The type of image is determined by the object distance.
do > 2 f
IMAGE = real, inverted, smaller F’ F F F’
2 f > do > f
IMAGE = real, inverted, bigger
do < f
IMAGE = virtual, upright, bigger F’ F

13. Copywrited by Holt, Rinehart, & Winston
Convex Lens

14. Concave Lens Ray Diagrams
All ray diagrams start with a center line and the lens
Note: the lens can be simplified into a straight vertical line

15. Locate and label the focal points:
F (real focal point) and F’ (virtual focal point)
The center (C) is located where the lens intersects the center line
Draw the object as described in the problem F’ F C

16. Concave Lens – Principal Rays
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Rays parallel to principal axis are refracted through the virtual focus (F’).
2. Rays through the real focus (F) are refracted parallel to the principal axis.
3. Incident rays along a secondary axis (through O) are not appreciably refracted.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.

17. You can only get 1 type of image from a concave (diverging) lens: virtual, upright, smaller
draw a ray in line with opposite F to the lens
THEN parallel to the center line
(2) draw a ray parallel to the center line to the lens
THEN in line with near F
(3) draw a ray through C F’ F
If refracted rays do not meet in “real” space, draw dashed lines back from refracted rays so that they intersect behind the lens

18. Concave Lens
Copywrited by Holt, Rinehart, & Winston