PhysicsLAB Resource Lesson
Diverging Lenses

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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.
 
 
Before continuing to a paper-and-pencil exercise in which you will construct the two special cases for diverging lenses, we are going to use the following physlet to examine the general properties of images formed by diverging lenses.
 
When the physlet opens notice that the author has listed for you the initial focal length, object distance and image distance. Notice that both the focus and image position are now negative. This signifies that they are located on the same side of the lens as the object. 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?

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.
 
Remember to review this lesson's complementary lesson on converging lenses.



 
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