PH 103

1
PH 103

• Dr. Cecilia Vogel
• Lecture 7

2
Review

• Lenses
• ray diagrams
• application to camera, eye
• more thin lens equation

Outline

• Lenses
• application to corrective lenses
• application to magnifier, microscope
• angular size and magnification

3
Vision Problems

• Near Point -- nearest distance your eye can focus
  
• Find yours
• problems if near point is gt 25 cm
• farsightedness
• Far Point -- farthest distance your eye can focus
  
• Do you know yours?
• problems if far point is lt many meters
• nearsightedness

4
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

5
Correcting Farsightedness
x
25 cm
Near point

• Use lens equation with
• do 25 cm - x
• di - (near point - x)
• negative, because virtual!

Example glasses 2cm from eye, near point is 45cm
6
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

7
Correcting Nearsightedness
Far point
x
Very far

• Use lens equation with
• do very large - x
• 1/do 0
• di - (far point - x)
• negative, because virtual!

8
Angular size

• Are stars big or small?
• Angular size is angle object makes at your eye
• depends on
• size of object
• distance away
• tan(q) ? q ? (size)/distance

• Can make an object seem bigger by bringing it
  closer
• Whats the limit?
• No closer than your nearpoint
• (or you cant see it clearly)

9
Magnifying glass

• 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

• Know image is
• upright
• farther, so bigger

• Therefore
• converging lens
• virtual, in front

• Must be Case I

10
Angular magnification

• What is angular size of image compared to angular
  size of the object when its at your nearpoint
• compared to the best you can do without
• Angular size of image
• hi/di

ho/do

• Angular size of object at your nearpoint
• ho/N
• So angular magnification
• M (ho/do)/(ho/N)

• M N/ do

11
Angular magnification

• General M N/ do

• Whats the best (biggest) you can do?
• Put the image at your nearpoint, di-N,
  doNf/Nf
• Maximum angular magnification
• Mmax 1N/f
• Whats the easiest on the eye?
• Put the image very far away, di-?, dof
• Relaxed-eye angular magnification
• Mrelax N/f

Example f 2.5 cm
Mrelax N/f 10
Mmax 1N/f 11