1. Light and Lenses
While Mirrors involve the reflection of light and the images we see, Lenses involve another property of light, refraction, or the effects of light entering a medium that propagates the wave at a different speed.
Lenses are probably the most important optical device and date to the 16th centuries.

2. Lenses we deal with here are thin lenses, which are usually part of a larger sphere, like the mirrors we discussed earlier.
Instead of having a reflective surface on one side, lenses will alter the path of the light wave by causing the wave to bend, focusing the light waves and producing images.
Lenses are either convex, or concave.

3. Convex lenses are also called converging lenses, as they take parallel light waves and make them converge at one point, the focus. Convergent lenses are thicker in the center than around the edges.
Concave lenses are also called divergent lenses, as they make parallel waves spread out from one point.

5. Convergent lenses

6. When rays parallel to the axis of a lens strike the lens, they are bent toward the axis at both surfaces of the lens. These parallel rays will be bent to a tiny point, the focal point (the image point for an object at infinity on the principal axis). The distance from the center of the lens to the focal point is focal length.
When they hit the lens from an angle, they will be bent toward a point that falls along a plane perpendicular to the axis of the lens called the focal plane.

7. Focal plane

9. Divergent lenses

10. The focal point F of a divergent lens, is the point from which refracted rays, originating from parallel incident rays, seem to emerge.
We can use rays to determine where the images will be when using lenses just as we did with mirrors.

11. Ray 1 parallel to x axis and refracted through F

12. Ray 2 through F’ and refracts leaving lens parallel to axis

13. Ray 3 through center of lens, emerging at same angle as it entered.

14. The image appears where the three rays converge, usually only two rays required to position image and third can be used as check.
Images that appear on the opposite side of the lens from the object are real images and those on the same side of the object are virtual.

15. Object placed inside focal length of converging lens.

16. Sign conventions with lenses
Focal length is positive for converging lenses and negative for diverging lenses.
Object distance is positive for objects that are on same side of lens as light. (usually the case except when combinations of lenses are used.)
Image distance is positive for real images (on opposite side of lens from object) or negative for virtual images (same side)
Heights are positive above axis and negative below.

17. The rays drawn for a divergent lens

18. Lens Equations
Using the conventions listed, we can use the same equations from mirrors for lenses:
= 1
do di f
Magnification :
m = hi = -di
ho do

19. Summary