1. 2/8/16Oregon State University PH 212, Class #161 The Thin-Lens Equation The thin lens approximation holds for a lens whose thick- ness is small compared to its focal length. With that assumption, plus some geometry and algebra, we can use this calculation for lenses: 1/d 0 + 1/d i = 1/f Definitions and sign conventions: Object distance (d 0 ): + when object is left of the lens (real); Image distance (d i ): + if the image is right of the lens (real); – if the image is left of the lens (virtual). Focal length (f): + for a converging lens. – for a diverging lens.

2. 2/8/16Oregon State University PH 212, Class #162 The Magnification Equation for Lenses The magnification equation for lenses is: m = h i /h o = –d i /d o where h o is the object height and h i is the image height (negative if the image is inverted with respect to the positive object height). The meaning of the sign of m: Assuming the object is upright: m is + if the image is upright. m is – if the image is inverted.

3. An object is placed 10.0 cm from a converging lens which has a focal length of 12.0 cm. What is the resulting magnification? 1.6.00 2.-6.00 3.2.00 4.-2.00 5.Not enough information. 2/8/163Oregon State University PH 212, Class #16 d o = 10, and f = 12, so:1/d i = 1/f – 1/d o Thus: d i = (d o )(f)/(d o – f) = (10)(12)/(10 –12) = –60 cm The image distance is negative, so the image is virtual, upright and enlarged—indeed, the only sort of virtual image that a converging lens (i.e. a lens with a positive f) can produce—which it does when the object distance is less than the focal length. The magnification eqn.: m = –d i /d o = –(–60/10) = (+)6.00

4. Formation of image with a Converging Lens summary: If object is located outside of focal point (d o > f ): - Image is inverted. - Image is real. - Image is enlarged if f < d o < 2f. - Image is reduced if d o > 2f. - Image is on opposite side of lens from object. - Examples: camera, eye, projector. If object is located inside of focal point (d o < f ): - Image is upright. - Image is virtual. - Image is enlarged. - Image is on same side of lens as object. - Example: magnifying glass. 2/8/164Oregon State University PH 212, Class #16

5. Figure 23.36 2/8/165Oregon State University PH 212, Class #16

6. Figure 23.39 2/8/166Oregon State University PH 212, Class #16

7. Formation of image with a Diverging Lens summary: - Image is upright. - Image is virtual. - Image is reduced in size. - Image is on same side of lens as object. 2/8/167Oregon State University PH 212, Class #16

8. Chapter Summary 23.4 2/8/168Oregon State University PH 212, Class #16

9. The real values of lenses and imaging, of course, are their uses: They help to correct our view of the world (make it possible to view it clearly). They help to enhance our view of the world (make it appear larger, more detailed). How? The key to understanding all multiple-lens imaging systems (including your own eyes) is simple: Light strikes the lenses in some order (first, second, third, etc.). The image produced by the first lens becomes the object for the next lens. 2/8/169Oregon State University PH 212, Class #16

10. At this point, be sure to read section 24.1 in the textbook. Then see also the After class 16 materials for examples of how multiple lens systems work in tandem. The image produced by the first lens becomes the object that sends light to the next lens. For example, look at Prep 5-6, items 4a and 4b… 2/8/1610Oregon State University PH 212, Class #16