Lenses

As shown and discussed in class, light refracts TOWARD a normal line (dotted line, perpendicular to surface of lens) when entering a more dense medium.

Note, however, that this direction of bend changes from down (with the top ray) to up with the bottom ray. This is due to the geometry of the lens. Look at the picture to make sure that this makes sense.


The FOCAL LENGTH (f) of a lens (or curved mirror) where the light rays would intersect, but ONLY IF THEY WERE INITIALLY PARALLEL to each other. Otherwise, they intersect at some other point, or maybe not at all!

The location of images can be predicted by a powerful equation:

1/f = 1/di + 1/do

In this equation, f is the theoretical focal length (determined by the geometry of the lens or mirror), do is the distance between the object and lens (or mirror) and di is the distance from lens (or mirror) to the formed image.

We find several things to be true when experimenting with lenses. If the object distance (do) is:

greater than 2f -- the image is smaller
equal to 2f -- the image is the same size as the object (and is located at a di equal to 2f)
between f and 2f -- the images is larger
at f -- there is NO image
within f -- the image is VIRTUAL (meaning that it can not be projected onto a screen) and it appears to be within the lens (or mirror) itself

If an image CAN be projected onto a screen, the image is REAL. Convex lenses (fatter in the middle) and concave mirrors (like the inside of a spoon) CAN create real images - the only cases where there are no images for convex lenses or concave mirrors are when do = f, or when do < f. In the first case, there is NO image at all. In the second case, there is a magnified upright virtual image within the lens.

Concave lenses (thinner in the middle) NEVER create real images and ONLY/ALWAYS create virtual images. This is also true for convex mirrors (like the outside of a spoon, or a convenience store mirror).

Play around with this applet:

http://www.physics.metu.edu.tr/~bucurgat/ntnujava/Lens/lens_e.html

Convex lenses (which are defined to have a positive focal length) are similar to concave mirrors.

Concave lenses (which are defined to have a negative focal length) are similar to convex mirrors.


This is a bit more complicated, but here are some images and information for mirrors:

http://www.physicstutorials.org/home/optics/reflection-of-light/curved-mirrors/concave-mirrors