From Last Time…

1. Object Lens Image Image Object From Last Time… Lenses and image formation Physics 208, Lecture 5

2. Thin-lens approximation: Ray tracing Image Optical Axis F Object F 1) Rays parallel to optical axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays through F emerge parallel to optical axis. Here image is real, inverted, enlarged Physics 208, Lecture 5

3. Object distance Image distance s s’ Object Image How are all these related? f f focal length Making an image Physics 208, Lecture 5

4. Question A magnifying glass of diameter 2 cm and focal length 5 cm is used to form an image of the sun. Approximately what is the image distance? 0.2 cm 1 cm 2 cm 2.5 cm 5 cm Physics 208, Lecture 5

5. Image size vs object size: Magnification = M = Magnification Objectheight Image distance Objectdist. Image height Physics 208, Lecture 5

6. Far away objects The moon is 3.8x108 m away, and 3.5x106 m diameter. I use a 1 m focal length lens to make an image of the moon. About what diameter is this image of the moon? 0.5 cm 1 cm 2 cm 10 cm 1 m Physics 208, Lecture 5

7. Image (real, inverted) Object Image (real, inverted) Image (virtual, upright) These rays seem to originatefrom tip of a ‘virtual’ arrow. Different object positions Physics 208, Lecture 5

8. Image (virtual, upright) These rays seem to originatefrom tip of a ‘virtual’ arrow. Virtual images objects closer to a converging lens than the focal length form a virtual image • Virtual image • can’t be recorded on film, • Can’t be seen on a screen. • But rays can be focused by another lens • e.g. lens in your eye (focus on retina) • e.g. lens in a camera (focus on film plane) Physics 208, Lecture 5

9. Do these rays come from real image, a virtual image, or an object? Can’t tell. Rays are exactly equivalent, and can be imaged by a lens in exactly the same way. Physics 208, Lecture 5

10. Virtual Image : thin-lens equation Image (virtual) Object Object distance s Focal length f ( >0 for converging lens ) Image distance s’ Object distance < focal length Negative image distance: image on same side as object Physics 208, Lecture 5

11. o  s’ s Magnifying glass Object at near point – biggest it can appear when in focus • Object closer than focal point • Lens produces virtual image • Light rays appear to originate from virtual image • Virtual image is used as object for eye lens. • Have moved object ‘closer’, while permitting eye to focus Image (virtual, upright) Physics 208, Lecture 5

12. Magnifying glass A magnifying glass has a focal length of 8 cm. It is 1 cm in front of your eye. What is the closest that you can hold it to a bug so that the bug is in focus (your eye has a near point of 25cm). 4 cm 6 cm 8 cm 12 cm 25 cm s=? 1cm Physics 208, Lecture 5

13. Magnifying glass: angular magnification • Without magnifying glass, • object is biggest at near point, ~ 25 cm. • Subtends angle • With magnifier • Object can be closer, at object distance s • Subtends angle • Angular magnification is • Increases with decreasing obj. dist. • Smallest obj. dist. is for image at near point: Physics 208, Lecture 5

14. Diverging lens Optical Axis Object Image Focal length defined to be negative Then thin-lens equation can be used: Physics 208, Lecture 5

15. Virtual image and diverging lens • Example: object at infinity • Rays appear to originate from focal point. • Result • Object has been (virtually) transported to a new location Physics 208, Lecture 5

16. Nearsightedness Object I can’t focus on this This, I can see Physics 208, Lecture 5

17. Fixing nearsightedness Object Physics 208, Lecture 5

18. Reading glasses Without my glasses, my far point is about 25 cm. What is the weakest (longest focal length) corrective lens (located at my eye) would let me read a newspaper holding it 50 cm away? Lens should form a virtual image closer to my eye. I can focus on image only if it is less than 25 cm away. Weakest lens moves it least, so image distance = -25 cm. -25 cm +25 cm -50 cm +50 cm -100 cm +100 cm Physics 208, Lecture 5

19. Diopters • Two lenses close together ~ • Single lens, “effective” focal length feff • Lens power P • Defined as with f in meters • Units of P are diopters • Two lenses close together Physics 208, Lecture 5

20. Far away objects The moon is 3.8x108 m away, and 3.5x106 m diameter. I use a 1 m focal length lens to make an image of the moon. About what diameter is this image of the moon? 0.5 cm 1 cm 2 cm 10 cm 1 m Not a very big image. How can It be made ‘bigger’? Look at the image with a magnifying glass! Physics 208, Lecture 5

21. Telescope: two lenses, object far away Objective: Forms real image of far-away object Eyepiece: Used as magnifying glass to examine image • Eyepiece forms virtual image • Real image formed on retina by your eye lens. Objective Eyepiece Physics 208, Lecture 5

22. Telescope angular magnification • Without telescope, distant planet subtends angle • Objective lens forms real image • Height • Used as object by eyepiece lens • Eyepiece • Forms virtual image at infinity (for relaxed eye) • Object must be at focal point • Subtends angle • Angular mag: Physics 208, Lecture 5

23. p q Virtual image ‘Object’ Eyepiece Compound Microscope Real, inverted, image Object Objective Object outside focal pointForms a real image Real image used as object for eyepiece.Eyepiece forms virtual image for eye. Physics 208, Lecture 5