The mathematics of lenses & image formation
| The Lens Equation |
 |
f is the focal length of the lens.
- f is positive for convex (converging) lenses.
- f is negative for concave (diverging) lenses.
do is the object distance.
- For real objects, it is positive.
di is the image distance.
- For real images, it is positive.
- For virtual images, it is negative.
| Magnification Equation |
 |
- hi is the height of the image.
- ho is the height of the object.
- M is negative when images are inverted.
- M is positive when images are upright.
- The absolute value of M tells you how many times larger the image is than the object.
- If the absolute value of M is less than one, the image is smaller than the object.
- If the absolute value of M is greater than one, the image is larger than the object.
Solving problems with the lens equation and ray tracing.
- A 0.10 meter high object is placed 10.0 cm in front of a convex
lens with a focal length of 5.0 cm. What is the image distance?
What is the magnification? Draw a ray diagram for this
situation.
- A 0.20 meter high object is placed 25 cm in front of a concave
lens with a focal length of -5.0 cm. What is the image distance?
What is the magnification? Draw a ray diagram for this
situation.
- A 0.12 meter high object is placed 30.0 cm in front of a
convex lens with a focal length of 10.0 cm. What is the image
distance? What is the magnification? Draw a ray diagram for this situation.
- A 0.05 meter high object is placed 5.0 cm in front of a convex lens with a focal length of 10.0 cm.. What is the image distance? What is the magnification? Draw a ray diagram for this situation.
For your project, you will apply The
Lens Equation to the human eye. You must decide what an
appropriate value for image distance is? What is the diameter of
an eye? Then you choose an object distance (the distance from the
eye to the object you are looking at). Calculate the
required focal length of your eye!
Made 17 May 2008
by Lori Andersen.