PH 103 Dr. Cecilia Vogel Lecture 8

Review Outline  Lenses  more corrective lenses  angular size and magnification  application to magnifier  Lenses  application to camera, eye  application to corrective lenses

Lens Power  Commented last time that a shorter focal length lens is stronger;  it causes the rays to change direction more.  Power of lens is defined as  Power = 1/f  To get power in Diopters (D),  use f in meters.  Your prescription will read in diopters.

Near and Far Points  Near Point -- nearest distance your eye can focus clearly  Far Point -- farthest distance your eye can focus clearly  Wearing glasses changes your effective nearpoint/farpoint  Correcting distance vision makes near vision worse;  correcting near vision makes distance vision worse. 

Nearpoint and Corrective Lenses  Suppose your near point without corrective lenses is N  and you wear lenses with focal length f <0 at a distance x from your eye.  What is the closest object you can clearly see when you are wearing these lenses?  REMEMBER that when you are looking THROUGH the lens, you are looking at the IMAGE, not the object!

Nearpoint and Corrective Lenses  What is the closest object you can clearly see when you are wearing these lenses?  … one where the IMAGE is at distance N.  Given f and knowing d i = - ( N-x ), we can find d o  ex: farpoint = 2m, glasses 2 cm from eye (we found f =-1.98 m). suppose also N =10 cm w/o lens. New N=10.3 cm

 Are stars big or small?  Angular size of object is angle object makes at your eye  depends on  size of object  distance away  tan(   (size)/distance  tan(  in rad, if small)    (size)/distance   IN RAD Angular size

   (size)/distance  You can make an object seem bigger by bringing it closer  What’s the limit?  Limit = No closer than your nearpoint, N  (or you can’t see it clearly)  Largest angular size = size/N  = best you can do with naked eye

Magnifying glass  Image is larger, but…  it is also farther away, so…  it doesn’t seem any larger  ??  Recall that reading glasses  make an image that is further, larger  than object.  Simple magnifier (aka magnifying glass) does the same thing  converging lens, case II, virtual image.

Magnifying glass  How is a simple magnifier useful  if the larger image is farther away?  Usually one of two ways it is useful: 1. Suppose you need to spend long periods looking at objects up close  to see fine details. E.g. jeweler  Your eyes would get tired and strained.  Unless you use a lens to make the image farther away, so your eye can relax.

Magnifying glass  How is a simple magnifier useful  if the larger image is farther away?  Usually one of two ways it is useful: 2. Suppose you would need to bring an object closer than your nearpoint  to see very fine details.  You can’t see the object that close clearly.  Unless you use a lens to make the image farther away, so your eye can see the IMAGE clearly.

 What is angular size of image  compared to the best you can do with naked eye?  Angular size of image:  h i /|d i | Angular magnification =h o /d o  Angular size of object at your nearpoint  h o /N  this is the best you can do with naked eye

 What is angular size of image compared to the best you can do with naked eye?  Angular size of image: Angular magnification M = N/ d o General h o /d o  best you can do with naked eye  h o /N  So angular magnification is ratio of these  M = (h o /d o )/(h o /N)

Angular magnification –special case:  What’s the easiest on the eye?  To have the image very far away  which means that d o near f.  Relaxed-eye angular magnification  M relax = N/f General: M = N/ d o

Angular magnification –special cases:  What’s the best (biggest) you can get?  Put the IMAGE at your nearpoint,  d i = - N  Find d o from lens eqn, plug in above  Maximum angular magnification  M max = 1+(N/f) General: M = N/ d o