Physics 202, Lecture 25Today’s Topics

Image Formation Real Image, Virtual Image, and No Image Ray Diagram Images Formed by:

Mirrors (reflection) Concave and Convex

Lenses (refraction) Converging and Diverging

Imaging Imaging: visible object optical device image

opticaldevice

visible object Image

object lights

image lights

No Image: No point to point correspondence

Image Aberration: Poorly focused imaged points

Note: If image can be formed, only two rays per point are necessary

Image Properties

Real Image: image lights actually passthrough image

Virtual Image: image lights appear to have come from the image

Real images can be formed on a screen.

Image properties to be concerned include location, real/virtual, reduced/enlarged,

upright/inverted, similar/distorted,…

Real and Virtual Images

Ray Diagrams If image can be formed, only two rays are necessary

to determine an image point. Useful rays:

Object ray pointing to the center (C) image ray inline with the object ray Object ray parallel to principal axis image ray “pointing to” a focal point (F) Object ray passing through a focal point image ray parallel to principal axis.

principal axis

C

optical device

F

F

O

I

Image Formation Equation and Magnification

Parametersp: object distanceq: image distanceh: object heighth’: image heightM: magnificationf: focal length

�

M = h'h

= − pq

= ff − p

�

1p

+ 1q

= 1f

q = fpp − f

If |M|<1 → Image < ObjectIf |M|>1 → Image > ObjectIf M<0 → Image ↓↑ ObjectIf M>0 → Image ↑↑ Object

Mirr

ors

and

Thin

Len

ses

Image Formed by Flat Mirrors Parametersp: object distanceq: image distanceh: object heighth’:image heightM: magnification

Properties: Image is virtual and behind the mirror. Object distance = image distance (|p|=|q|) Lateral magnification M=1 Image is upright (for upright object) Image has front/back reversal.

1

0,0'

=−==

<>

pq

hhM

qp

Image Formed by Convex Mirror

Quiz 1: Is there another convenient ray to use? Quiz 2:

1. Real or virtual?2. Upright or inverted?3. Enlarged or reduced?

Answer: Virtual, upright (M>0), reduced (|M|<1)

�

f = R /2 < 01p

+ 1q

= 1f

q = fpp − f

< 0

0 < M = − qp

<1

R

Image Formed by Concave Mirrors

Object (O) in between F and Mirror:virtual, upright, enlarged

Object in front of Mirror:real, inverted. Enlarged orreduced, depending on p.

pq

hhM

fqp

Rf

−==

=+

=

'

1112/

Image Formed by Refraction

pq

hhM

Rnn

qn

pn

−==

−=+

'

1221

Closer, not-inverted, reduced, virtual…

R= ∞q= - p(n2/n1)M=-q/p =n2/n1<1

Example: looking at a fish

Thin Lenses Lenses are refractive optical devices with two

spherical sides.

Thin

R1 R2

f1

)11)(1(1

21 RRn

f−−=

Lens maker’s equation

F1,F2: Focal pointsf=f1=f2 Focal length

f2

f>0: convergingf<0: diverging

Converging and Diverging Lenses

sign convention:f<0

sign convention:f>0

Images Formed by Converging Lens

Object (O) is in front of F1 : real, inverted, enlarged or reduced

Object (O) in between F1 and lens: virtual, upright, enlarged.

pq

hhM

fqp

f

−==

=+

>

'

1110

pq

hhM

fqp

f

−==

=+

>

'

1110

Images Formed by Diverging Lenses

Images are always virtual, upright, and reduced

Images Formed by Diverging Lenses

Images are always virtual, upright, and reduced

pq

hhM

fqp

f

−==

=+

<

'

1110

Sign Conventions

>0 <0f concave mirrors

converging lensconvex mirrorsdiverging lens

p object side the other sideq real virtual

M=-q/p upright inverted

Real Virtualmirrors front behindlenses behind front