Lenses:  Enough already on mirrors.  Let’s talk about lenses.

Lenses refract light in a sort of organized way.  The type of lenses that we’ll be looking at are called double spherical lenses – both sides have the same radius of curvature.  Two types:

·       Concave lenses - cave inward

o      Aka: diverging lenses because the light rays always  diverge

o      only form virtual images.

·       Convex lenses - bulge outward

o      Aka: converging lenses because the refracted rays that pass through can converge.

o      can form real or virtual images.

Lens Stuff:  Here is the geometry of the double convex lens.

Q is the center of the lens, f and f’ are the focal points on either side of the lens.  Also note the line containing f & f’ is the principle axis.

Here are the rules for image formation:

·       Rays that are parallel to the principle axis are refracted through the focal point on the opposite side of the lens.

·       Rays the travel through the center of the lens are not refracted and travel in a straight line.

·       Rays that travel through the focal point before they reach the lens are refracted out of the lens parallel to the principle axis.

Ray 1 is the parallel ray that is refracted through focal point on the opposite side of the lens. 

Ray 2 is the ray that goes through the center of the lens.  

Ray 3 is the ray that goes through the focal point and is then refracted parallel to the principle axis.

The image is formed where the rays intersect.  As you can see this will be a real image.

Converging lenses form real images, they can also form virtual images as well.  This is what happens when you use one as a magnifying glass.

Here is a virtual image formed by a converging lens.  Notice that the object is inside the focal point.

When an object is placed at the focal point no image forms.  This is because all the rays are refracted so that they are parallel to one another.  They never cross, so they form no image.