1

23 Mirrors & Lenses

• Mirrors

• Lenses

• Lens Maker Equation

• 43, 67, 85, 89, 92, 93.

2

Images

• Real: light converges to a point.

• Ex. magnifying glass used to start fire.

• Virtual: light diverges (or appears to have diverged) from a point.

• Ex. Any “.” on this screen can be seen anywhere in room.

3

Ray Diagrams• axis, focal point/plane, mirror plane/V

• r, focal distance f = r/2

• do, di, f

4

concave mirror images

Animated Mirror Diagrams

• http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l3d.html

6

convex mirror images

• always “virtual”, “upright”, “diminished”

7

Mirror Equations

• relate do, di & f.

• lateral magnification (LM) = hi/ho.

you must learn the sign conventions to use these formulas

fdd io

111

o

i

o

i

d

d

h

hLM

8

Plane Mirror: Virtual Image

• di = -do

• f = infinity

9

Ex. Object sits 25cm in front of concave mirror with f = 15cm. Calculate the image distance and magnification. Check with a ray diagram.

10

thin lenses

• symmetric focal points

• converging (f>0), diverging (f<0)

11

converging lens rays

12

converging lens images

13

diverging lens images

14

lens power

• power = 1/(focal-length(meters))

• unit: [D, diopters, 1/m]

• used for corrective lenses

• Ex. near-sighted person P = -5.0Df = 1/P = 1/(-5) = -0.2m = -20cm.

15

Summary

• mirror & lens parameters

• ray diagramming, image formation and characterization

• calculation of parameters

16

Paraxial Approximation

• Focus isn’t exact for a spherical mirror (but rays near axis focus well)

• Focus is sharp for parabolic mirror (aspheric)

17

??do?? #43

• Silvered sphere R = 20cm, f = -10cm

• hi = 1/3 ho

• LM = hi/ho = -di/do = 1/3. -3di = do

• 1/do + 1/di = 1/f

• 1/(-3di) + 1/di = 1/(-10)

18

??do?? #67

• f = +10cm lens, what do causes LM = -2.

• LM = hi/ho = -di/do = -2 di = 2do

• 1/do + 1/di = 1/f

• 1/do + 1/2do = 1/10

19

imbedded object

• image distance < object distance

• s’ = s/n

20

Lens Maker’s Equation

21

111

RRn

nn

f o

o

• Ex. radii = 20cm, n = 1.5, in air & water: