1. PH 103 Dr. Cecilia Vogel Lecture 16

2. Review Outline  Lenses  ray diagrams  images  thin lens equation  Lenses  application to camera, eye, and corrective lenses  more thin lens equation

3. Camera and Eye  Know image is:  behind the lens, real  closer to lens, so |m|<1, so smaller  Therefore:  converging lens  inverted image  Must be Case III

4.  Eye:  change focal length of eye  relaxed eye, focal length longest, view distant object  tensed eye, focal length shortest, view nearby object  Camera:  move lens between object and image points  demo How to focus Image

5. Vision Problems  Near Point -- nearest distance your eye can focus  Find yours  problems if near point is > 25 cm  farsightedness  Far Point -- farthest distance your eye can focus  Do you know yours?  problems if far point is < many meters  nearsightedness

6. Correcting Farsightedness Want: Object at 25 cm to have an image at nearpoint  Know image is:  upright  farther from lens, therefore bigger  Must be Case I  Therefore:  converging lens  image in front, virtual

7. Correcting Farsightedness Use lens equation with  d o = 25 cm - x  d i = - (near point - x)  negative, because virtual! x 25 cm Near point Example: glasses 2cm from eye, near point is 45cm

8. Correcting Nearsightedness Want: Object far away to have an image at farpoint  Know image is:  upright  closer, so smaller  Must be Case IV  Therefore:  diverging lens  image is virtual, in front

9. Correcting Nearsightedness Use lens equation with  d o = very large - x  1/d o = 0  d i = - (far point - x)  negative, because virtual! x Far point Very far

10.  Are stars big or small?  Angular size is angle object makes at your eye  depends on  size of object  distance away  tan(   (size)/distance Angular size  Can make an object seem bigger by bringing it closer  What’s the limit?  No closer than your nearpoint  (or you can’t see it clearly) rad!

11. Magnifying glass  Know image is:  upright  farther  Therefore:  converging lens  virtual, in front  Must be Case I  Use a lens as magnifier:  Can bring object closer to eye than nearpoint  to make it even bigger  So long as the image is farther than nearpoint

12.  What is angular size of image compared to angular size of the object when it’s at your nearpoint  compared to the best you can do without  Angular size of image:  h i /|d i | Angular magnification M = N/ d o =h o /d o  Angular size of object at your nearpoint  h o /N  So angular magnification  M = (h o /d o )/(h o /N)

13. Angular magnification  What’s the best (biggest) you can do?  Put the image at your nearpoint, d i =-N, d o =Nf/N+f  Maximum angular magnification  M max = 1+N/f  What’s the easiest on the eye?  Put the image very far away, d i =- , d o =f  Relaxed-eye angular magnification  M relax = N/f General: M = N/ d o Example f = 2.5 cm M max = 1+N/f = 11 M relax = N/f =10