1. Converging Lenses
Mrs. Scheitrum

2. What is a Lens?
A lens is a piece of transparent material that refracts light rays such that it forms an image.
There are different types of lenses:
Converging
Diverging
Today, we are only looking at converging lenses.

3. Converging Lens
For the purpose of this class, we will look only at lenses that are symmetrical across their principal axis (horizontal).
Converging lens – a lens that converges rays of light that are traveling parallel to its principal axis.
Thick at the principal axis and thin at the edges.

4. Converging Lenses
Double Convex Lens

5. Key Terms
Principal axis – The imaginary line that runs horizontally and divides the lens symmetrically.
Focal point – the point at which light converges (for a converging lens).
Vertical axis – divides the lens in half vertically.
Focal length (F) – the distance from the lens to the focal point.

7. Refraction Revisited
When light passes from one boundary to another, it is refracted.
This is true of lenses as well, causing the change in location of the image.
How do we know where the image will be formed?

8. Refraction Revisited
We can construct ‘ray diagrams’ of incident light rays in order to determine the image location.
Note that the following rules are only true for thin lenses!

9. For Simplicity…
We can assume that all objects take the form of an arrow… 2F F F 2F

10. Rules of Refraction – Rule #1
Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens. 2F F F 2F

11. Rules of Refraction – Rule #2
Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. 2F F F 2F

12. Rules of Refraction – Rule #3
An incident ray that passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens. 2F F F 2F

13. Rules of Refraction – Image Location
The image will appear where these lines intersect. 2F F F 2F

14. Objects Located at the Focal Point

15. Examples
Turn to the Ray Diagram side of the handout.

16. Mathematics of Lenses
As always, there are equations that can help us solve for missing variables.
These equations should look very familiar…

17. Mathematics of Lenses
The Lens Equation
Magnification Equation

18. Sign Conventions f is + if the lens is a converging lens.
f is – if the lens is a diverging lens.
di is + if the image is a real image and located on the opposite side of the lens.
di is – if the image is a virtual image and located on the object’s side of the lens.
hi is + if the image is an upright image (virtual).
hi is – if the image is an inverted image (real).

19. Examples
Turn to the Problems side of the handout.

20. Assignment
Page 496, Problems 15-19