#### Differences between lenses and mirrors

• Light reflects from a mirror. Light goes through, and is refracted by, a lens.

• Lenses have two focal points, one on either side of the lens.

• A concave mirror converges light to a focal point. For lenses, light converges to a point for a convex lens. A convex mirror diverges light, as does a concave lens.

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 equations we used for mirrors all work for lenses.

• A convex lens acts a lot like a concave mirror. Both converge parallel rays to a focal point, have positive focal lengths, and form images with similar characteristics.

• A concave lens acts a lot like a convex mirror. Both diverge parallel rays away from a focal point, have negative focal lengths, and form only virtual, smaller images.

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:

• The parallel ray goes from the tip of the object horizontally to the lens. It refracts through the lens and passes through the focal point on the far side of the lens.

• The chief ray is a straight line starting from the tip of the object and passing through the center of the lens. As long as the lens is thin we can assume the ray passes straight through.

• The focal ray is a mirror image of the parallel ray. It goes from the tip of the object through the focal point on the object side of the lens, and emerges from the lens going parallel to the principal axis.

#### 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?

• The parallel ray goes from the tip of the object horizontally to the lens. It refracts through the lens and diverges away from the principal axis going directly away from the focal point on the object side of the lens.

• The chief ray is a straight line starting from the tip of the object and passing through the center of the lens. As long as the lens is thin we can assume the ray passes straight through.

• The focal ray leaves the tip of the object heading toward the focal point on the far side of the lens. It is re-directed by the lens to go parallel to the principal axis.

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.