Converging Lenses
Any lens that is "thicker in the center" than on the edges is generally described as a convex lens and will function as a converging lens when it is operating in air.

The point where all rays which enter the lens parallel to its axis are brought to a focus is called the principal focus. This position is located behind the lens and is usually labeled as F in ray diagrams. A similar point the same distance in front of the lens is called the lens' secondary focus, F'. The distance from the center of the lens to the principal focus is called the focal length of the lens and is represented by the variable, f.

Whenever the actual rays of light that refract through the lens converge behind the lens to form an image, that type of image is called a real image. Real images can be projected onto a screen, are always inverted and reversed left-to-right. For those of you who have ever loaded a slide projector, you know that you must first flip-over and then rotate each slide to insure that the image on the screen will be correctly oriented.

Since the actual rays of light passing through the lens form these real images, they are also known as "hot" images. Remember, that each ray of light is composed of photons which are packets of radiant energy. If you have ever tried to use a magnifying glass to burn a hole in a dried leaf or roast a small piece of a hot dog, then you have experienced this property of real images. You instinctively learned to place the leaf or hot dog at the principal focus of the magnifying glass' converging lens.

Converging Lenses

There are three primary rays which are used to locate the images formed by converging lenses. Each ray starts from the top of the object.

 Ray #1(aqua) runs parallel to the axis until it reaches the lens; then it refracts through the lens and leaves along a path that passes through the lens' principal focus Ray #2(gold) runs straight through the center of the lens never bending Ray #3(pink) first passes through the secondary focus until it reaches the lens; then it refract through the lens and leaves parallel to the lens' axis on the other side of the lens
Remember, ALL rays must have ARROWS! When all three of these rays meet, they will form the image.

Before continuing to a paper-and-pencil exercise in which you will construct six special cases for converging lenses, we are going to use the following physlet to examine the general properties of images formed by converging lenses.

When the physlet opens notice that the author has listed for you the initial focal length, object distance and image distance. Move the object as far to the left as possible and then notice the position, orientation, and size of  the image that is formed as you move the object towards the lens.

 What happens to the position, orientation, and size of the image as the object approaches a location just ever-so-slightly greater than 1 meter in front of the lens (the principal focus)? Are these images real or virtual?

 What happens to the position, orientation, and size of the image when the object is placed exactly 1 meter in front of the lens?

 What happens to the position, orientation, and size of the image when the object is placed between the principal focus and the center of the lens? Are these images real or virtual?

 SIX special ray diagrams for converging lenses   Each of the following animated gifs repeats itself 5 times and then stops. If you wish to restart them, press F5. In each of these diagrams,   Region I is greater than two focal lengths in front of the lens. Region II is between one and two focal lengths in front of the lens, Region III is within one focal length in front of the lens; and, conversely Region IV is within one focal length behind the lens, Region V is between one and two focal lengths behind the lens, and Region VI is beyond two focal lengths behind the lens. Case #1: object is located at infinity. Case #2: object is located in region I. Case #3: object is located on the line between regions I and II, exactly two focal lengths in front of the lens. Case #4: object is located in region II. Case #5: object is located on the line between regions II and III, exactly one focal length in front of the lens. Case #6: object is located in region III.   In Case #6, the three rays diverged, so that you had to "dot back" their refracted segments. This created a virtual image which was upright and located on the same side of the lens as the object.   Remember that converging lens always form real images EXCEPT when the object is initially placed within the focal length. Then the lens acts like a magnifying glass and produces an enlarged virtual image.   Remember to review this lesson's complementary lesson on diverging lenses.