10.14 Image formation by lenses  (Page 9/18)

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.

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 $f$ .
• Power $P$ of a lens is defined to be the inverse of its focal length, $P=\frac{1}{f}$ .
• 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 $\frac{1}{d_{\text{o}}}+\frac{1}{d_{\text{i}}}=\frac{1}{f}$ and $\frac{h_{\text{i}}}{h_{\text{o}}}=-\frac{d_{\text{i}}}{d_{\text{o}}}=m$ (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.