Converging Lens :-
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 |
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.
Diverging Lens :-
| Any lens that is "thinner in the center" than on the edges is called a concave lens and will function as a diverging lens when operating in air. The point where rays which entered the lens parallel to its axis are brought to a focus in front of the lens is called the principal focus. This position is usually labeled F in ray diagrams. A similar point the same distance behind the lens is called the lens' secondary focus, F'. When the actual rays of light diverge after passing through the lens, the image formed by the intersection of their "dotted back segments" is called a virtual image. Virtual images are always upright images which are "trapped" inside the lens. Since the actual rays of light do NOT form these images, virtual images are also known as "cool" images. This type of image can NOT be projected onto a screen.
Diverging Lenses
There are three primary rays which are used in ray diagrams to locate images formed by diverging lenses. Each of these rays start on the top of the object.
Ray #1
(aqua) | runs parallel to the axis, refracts through the lens so that, when dotted back, it passes through the principal focus | Ray #2
(gold) | runs straight through the center of the lens never bending | Ray #3
(pink) | aims for the secondary focus, refracts through the lens and runs off parallel to the axis on the other side of the lens | Remember, ALL rays must have ARROWS indicating the forward direction of the light rays. When all three of these diverging rays are dotted back, they form a virtual image. TWO special ray diagrams for diverging 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 an infinite distance from the lens Case #2: object is located anywhere in either Regions I, II, or III In all cases, the three rays diverge when refracted through a diverging lens. You must always "dot back" their refracted segments to form a virtual image. These images are always upright, reduced and located on the same side of the lens as the object between the lens and the object.
Remember that converging lens ONLY form virtual when the object is initially placed within one focal length. Then the lens acts like a magnifying glass and produces an enlarged virtual image. Whereas, diverging lenses ALWAYS form reduced, virtual images in regions I, II, or III.
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