Physics 203/204Physics 203/204

4: Geometric Optics

•Images formed by refraction•Lens Makers Equation•Thin lenses•Combination of thin lenses•Aberration•Optical Instruments

Images formed by Refraction

1

2

for 1 and 2 small ( paraxial rays)

n1

s

n2

s

n2

n1

R

s s’

R

Real Object s positive in front ofsurface

VirtualObject s negative behind

surface

Real Image s' positive behindsurface

Virtual Image s' negative in front ofsurface

Real centerof curvature

Virtual centerof curvature

R positive

R negative

behindsurface

in front ofsurface

For plane surfaces

n1

s

n 2

s s = -

n 2

n1

s ( virtual image)

n 2

n1

relative index of refraction

• Thin Lenses•Image formed by one refracting surface is •Object of second surface

s1

s’1

s2

I1

I2

medium 1

medium 2

assume n1 1 and use the preceding equation

1s1

1s 2n-1 1

R1 1R2

1

s1

s for thin lenses

s’2

The focal length of a lens is defined as

the image distance S' when the object is

at , i.e. f= s when s=.

1f1

s 1

s n-1 1

R1 1R2

Lens Maker Equation

A thin lens has 2 focal points depending on

whether incident rays come from left or right.

Lateral magnification = m=h

h s

s

Lenses

Double Convex

Plano Convex

Convexmeniscus

DoubleConcave

PlanoConcave

ConcaveMeniscus

Type of Lens Object Distance asCompared to Focal

Length

Characteristics of Image

Convex d > 2f real, inverted, diminshed

d = 2f real, inverted, same size

f < d < 2f real, inverted, magnified

d=f no image formed

d < f virtual,erect,magnif ied

Concave for any d virtual, erect, diminished

•Focal length is positive for converging lenses and negative for diverging lenses.•Object distance is positive if it is on side of lens that light is coming from (not always true!)•Image distance is positive if it is on the opposite side of lens that light is coming from.•Object and image heights are positive above the axis, negative below.

o F I

1

2

•Ray 1 (appears to) come from focal point•Ray 2 passes through center of lens

Combination of thin lenses

1

s 1

s 1

f1

1

f2

s= object distance from first lens

s = image distance from second lens

if the lenses are touching they act as

a single lens with focal length

1

f = 1

f1

1

f2

Lens Aberrations

Lens and mirror equations assume ray makes small angle with optic axis, if this

is not the case, imperfect blurred images are formed, this is called

ABERRATIONS

spherical aberration

chromatic aberration

•Other Aberrations•Astigmatism

•point object off the axis produces two line

images

at different points.•Coma

•off axis object produces a coma shaped image•Distortion

•magnification for off axis points different than

for

on axis points

Optical Instruments

•Camera•The light intensity I incident on the film per unit area is inversely proportional to the square of the ratio of the diameterof the lens to its focal length. The f-number equals the ratio of the focal length to the lens diameter

I 1fD 2

; f- number = fD

•Eye•The power of a lens in Diopters is the reciprocal of the focal length measured in meters (including sign)

p 1

f

•Simple Magnifier•When an object is at the near point of the eye ( 25 cm) the angle subtended by the object is When a convex lens of focal length f is placed between the eye and the object an image which subtends an angle 0 can be formed at the near point

angular magnification

m =0

1 25f

•Compound Microscope•objective focal length of f0

•eye piece of focal length fe

•the two lenses are separated by a distance L •For object located just beyond focal point of objective, the two lenses combined form an enlarged virtual and inverted image of lateral magnification M

M =-

Lf 0

25

f e

•Astronomical telescope•Two convex lenses are separated by a distance equal to the sum of their focal lengths. The angular magnification is equal to the ratio of the two focal

lengths

m

f0

f e