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