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Three types of images formed by thin lenses
Type Formed when Image type d i m
Case 1 f size 12{f} {} positive, d o > f size 12{d rSub { size 8{o} }>f} {} real positive negative
Case 2 f size 12{f} {} positive, d o < f size 12{d rSub { size 8{o} }<f} {} virtual negative positive m > 1
Case 3 f size 12{f} {} negative virtual negative positive m < 1 size 12{m<1} {}

In Image Formation by Mirrors , we shall see that mirrors can form exactly the same types of images as lenses.

Take-home experiment: concentrating sunlight

Find several lenses and determine whether they are converging or diverging. In general those that are thicker near the edges are diverging and those that are thicker near the center are converging. On a bright sunny day take the converging lenses outside and try focusing the sunlight onto a piece of paper. Determine the focal lengths of the lenses. Be careful because the paper may start to burn, depending on the type of lens you have selected.

Problem-solving strategies for lenses

Step 1. Examine the situation to determine that image formation by a lens is involved.

Step 2. Determine whether ray tracing, the thin lens equations, or both are to be employed. A sketch is very useful even if ray tracing is not specifically required by the problem. Write symbols and values on the sketch.

Step 3. Identify exactly what needs to be determined in the problem (identify the unknowns).

Step 4. Make a list of what is given or can be inferred from the problem as stated (identify the knowns). It is helpful to determine whether the situation involves a case 1, 2, or 3 image. While these are just names for types of images, they have certain characteristics (given in [link] ) that can be of great use in solving problems.

Step 5. If ray tracing is required, use the ray tracing rules listed near the beginning of this section.

Step 6. Most quantitative problems require the use of the thin lens equations. These are solved in the usual manner by substituting knowns and solving for unknowns. Several worked examples serve as guides.

Step 7. Check to see if the answer is reasonable: Does it make sense ? If you have identified the type of image (case 1, 2, or 3), you should assess whether your answer is consistent with the type of image, magnification, and so on.

Misconception alert

We do not realize that light rays are coming from every part of the object, passing through every part of the lens, and all can be used to form the final image.

We generally feel the entire lens, or mirror, is needed to form an image. Actually, half a lens will form the same, though a fainter, image.

Section summary

  • Light rays entering a converging lens parallel to its axis cross one another at a single point on the opposite side.
  • For a converging lens, the focal point is the point at which converging light rays cross; for a diverging lens, the focal point is the point from which diverging light rays appear to originate.
  • The distance from the center of the lens to its focal point is called the focal length f size 12{f} {} .
  • Power P size 12{P} {} of a lens is defined to be the inverse of its focal length, P = 1 f size 12{P= { {1} over {f} } } {} .
  • A lens that causes the light rays to bend away from its axis is called a diverging lens.
  • Ray tracing is the technique of graphically determining the paths that light rays take.
  • The image in which light rays from one point on the object actually cross at the location of the image and can be projected onto a screen, a piece of film, or the retina of an eye is called a real image.
  • Thin lens equations are 1 d o + 1 d i = 1 f and h i h o = d i d o = m size 12{ { {h rSub { size 8{i} } } over {h rSub { size 8{o} } } } = - { {d rSub { size 8{i} } } over {d rSub { size 8{o} } } } =m} {} (magnification).
  • The distance of the image from the center of the lens is called image distance.
  • An image that is on the same side of the lens as the object and cannot be projected on a screen is called a virtual image.

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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