Differences between lenses and mirrors

Any lens that is thicker in the center than the ends is a convex lens. Any lens thicker at the ends than in the center is a concave lens.

Similarities between lenses and mirrors

The sign convention is just a little different. Because the light goes through the lens positive image distances (and real images) are on the opposite side of the lens from the object. Negative image distances are for virtual images, again, but those are on the same side of the lens as the object.

Converging lens:
Concave Mirror:
Diverging lens:
Convex Mirror:

Ray Diagram for a Convex Lens

Once again, a ray diagram can help us understand what a lens does. Send rays out from the object, refract them through the lens, and see where they go. The image is where the rays intersect.

Rays that are easy to draw include:

Image Characteristics for a Convex Lens

The table shows what happens to the image as an object is brought from infinity toward a convex lens.

Object PositionImage PositionImage Characteristics
At infinityAt focal pointImage is a point
Moving toward 2FMoving from F toward 2FIncreasing in size, real, inverted, smaller than object
At 2FAt 2FReal, inverted, same size as object
Moving from 2F toward FMoving from 2F toward infinityReal, inverted, larger than the object
At FAt infinityInfinitely big
Moving from F toward lensMoving from -infinity toward lensDecreasing in size, virtual, upright, larger than the object

As long as the image as real the ray diagram is reversible. An object at point A creates an image at point B, while an object at point B creates an image at point A.

Ray Diagram for a Concave Lens

What happens with a concave lens?

Moving an object from infinity toward a concave lens gives an image that moves from the focal point toward the lens, growing from a point to almost as large as the object. The image is virtual, upright, and smaller than the object.