# 25.6 Image formation by lenses  (Page 10/19)

 Page 10 / 19

## Test prep for ap courses

An object is 25 cm in front of a converging lens with a focal length of 25 cm. Where will the resulting image be located?

1. 25 cm in front of the lens
2. 25 cm behind the lens
3. 50 cm behind the lens
4. at infinity (either in front of or behind the lens)

(d)

A detective holds a magnifying glass 5.0 cm above an object he is studying, creating an upright image twice as large as the object. What is the focal length of the lens used for the magnifying glass?

A student wishes to predict the magnification of an image given the distance from the object to a converging lens with an unknown index of refraction. What data must the student collect in order to make such a prediction for any object distance?

1. A specific object distance and the image distance associated with that object distance.
2. A specific image distance and a determination of whether the image formed is upright or inverted.
3. The diameter and index of refraction of the lens.
4. The radius of curvature of each side of the lens.

(a)

Given a converging lens of unknown focal length and unknown index of refraction, explain what materials you would need and what procedure you would follow in order to experimentally determine the focal length of the lens.

## 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.

## Conceptual questions

It can be argued that a flat piece of glass, such as in a window, is like a lens with an infinite focal length. If so, where does it form an image? That is, how are ${d}_{\text{i}}$ and ${d}_{\text{o}}$ related?

You can often see a reflection when looking at a sheet of glass, particularly if it is darker on the other side. Explain why you can often see a double image in such circumstances.

When you focus a camera, you adjust the distance of the lens from the film. If the camera lens acts like a thin lens, why can it not be a fixed distance from the film for both near and distant objects?

A thin lens has two focal points, one on either side, at equal distances from its center, and should behave the same for light entering from either side. Look through your eyeglasses (or those of a friend) backward and forward and comment on whether they are thin lenses.

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