[PDF] 31Image formation by Mirrors and Lenses - Physics Courses





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limite-et-continuité.pdf

p.f(a) + q.f(b)=(p + q).f(c). Exercice 19 [ 01808 ] [Correction]. Notre objectif dans cet exercice est d'établir la proposition :.





31Image formation by Mirrors and Lenses - Physics Courses

pqf = 1?1 qf p Real =fp =(10)(30) ?=15cmpf30 ?10 =? q=? 15=?0 5p30 InvertedReduced Example An object is placed 30 cm in front of a diverginglens with a focal length of -10 cm Find the image distance and magnification + 1=1 pqf = 1?1F qf p10 cm fp( ?10)(30)30 cm == =?7 5cmp?f30 ??( 10)Virtual image =? =? ?=q7 5M 0 25 30 Upright imagereduced



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Rt The iff - Purdue University

Probability measures P and Q on S coincide if Pf Qf t f e BCS Roof of Theorem 1 2 Suppose that for any closed AES we are able to find a function f e BC S such that I



Notes on Convergence of Probability Measures by Billingsly

gives Qf QF Stringing these together gives PF QF akingT to zero gives PF QF(like in the last theorem QF !QF) Of course the argument works equally well to show QF PF so we get the desired result De nition 7 We say that a probability measure P on S is tight for every >0 there exists a compact set Kso that PK>1 This notion of tight is a

1

3.1 Images formed by Mirrors and Lenses

• Images • Image formation by mirrors • Images formed by lenses

Object-Image

• A physical object is usually observed by reflected light that diverges from the object. • An optical system (mirrors or lenses) can produce an image of the object by redirecting the light. - Real Image - Virtual Image

Real ImageObject

real Image

Optical System

diverging converging diverging

Light passes through the real image

Film at the position of the real image is exposed.

Virtual ImageObject

virtual ImageOptical System diverging di ve r g in gLight appears to come from the virtual image but does not pass through the virtual image Film at the position of the virtual image is not exposed.

Image formed by a plane mirror.

The virtual image is formed

directly behind the mirror.

Light does not

pass through the imageObject Image

Each point on the image can be determined

by tracing 2 rays from the object. mirrorB B' A

A'object

image p q A virtual image is formed by a plane mirror at a distance q behind the mirror. q = -p 2

Parabolic Mirrors

Parallel rays reflected by a parabolic mirror are focused at a point, called the

Focal Point located on the optic axis.

Optic Axis

Parabolic Reflector

Parabolic mirrors can be used to focus incoming parallel rays to a small area or to direct rays diverging from a small area into parallel rays.

Spherical mirrors

•Spherical mirrors are much easier to fabricate than parabolic mirrors • A spherical mirror is an approximation of a parabolic mirror for small curvatures. (i.e. for paraxial rays -close to parallel to the optic axis. • Spherical mirrors can be convex or concave light light concave convex

Parallel beams focus at the focal point of

a Concave Mirror.

Focal point

Ray tracing with a concave spherical mirrors

• A ray parallel to the mirror axis reflects through the focal point, F which is at a point half the radius distance from the mirror along the optic axis.

• A ray passing through the focal point reflects parallel to the mirror axis • A ray striking the center of the mirror reflects symmetrically around the mirror axis • A ray that passes through the center of curvature Creflects and passes back through itself FC

Mirror

axis RF2

Law of

Reflection

The position of the image can be

determined from two rays from the object. F C

The image is real, inverted, reduced

When object distance > C

3

A concave mirror can form real and

virtual images

O > CC > O > FF > O

Real

Inverted

ReducedReal

Inverted

EnlargedVirtual

Upright

Enlarged

Simulation of image formation by a

mirror PHYSLETS were developed at Davidson University by Wolfgang Christian.

Question

What image of yourself do you see when

you move toward a concave mirror?

Far away

Real image

Inverted

Reduced

CReal image

Inverted

Magnified

O~F

Magnified Image

Real or Virtual?

4 OVirtual Image

Upright

Enlarged

Convex Mirror

Image is virtual, upright, reduced

Ray parallel to the optic axis

reflects so that the reflected ray appears to pass through the focal point.

Focal Point

A Convex Mirror always forms

virtual images virtual, upright, reduced virtual, upright, reduced

Question

Describe how your image would appear as

you approach a convex mirror?

Virtual Image

Upright

The image is

reduced in size and the field of view is larger.Virtual Image

Upright

5

Virtual Image

Upright

Mirror Equation

f O I p q 111
pqf p is positivefor real objects. f is positive if the light from infinity goes through the focal point. f positivefor concave mirrors, f negativefor convex mirrors q is positiveif the light goes through the image -real image q is negativeif light does not go through image -virtual imagep - object distance q - image distance f - focal length

Magnification

f O I p q 'hqMhp h h' q -positive - image is real

M is negative - the image is inverted.

Magnification

f O I p q hqMhp h h' q is negative - the image is virtual

M is positive - the image is upright.

Question

A boy stands 2.0 m in front of a concave mirror with a focal length of 0.50 m. Find the position of the image. Find the magnification. Is the image real or virtual? Is the image inverted or erect?

p O I q 111
pqf

111qfp

fpqpf

0.5(2.0)0.672.0 0.5m

qmp

0.670.332.0

Real image

inverted

Image formed by refraction

• Light rays are deflected by refraction through media with different refractive indexes. • An image is formed by refraction across flat or curved interfaces and by passage through lenses. 6

Image formed by Refraction

oo

Image of the tip

Image formed by refraction through

a refracting surface.

Real image formed by refraction.Light is

caused to

Converge.

Rotation

of the ray at the interface

Converging Lenses

Fatter in the middle.

Cause light to converge toward the optic axis

Diverging Lenses

Thinner in the middle

Cause light to diverge away from the optic axis

Parallel light though a converging

lens is focused at the focal point.

A real image is formed

Ray tracing for lenses

• A line parallel to the lens axis passes through the focal point • A line through the center of the lens passes through undeflected. f 7

Ray diagram for a converging

lenses

ObjectImage

A converging lens can form real

and virtual images converging light converging light diverging lightReal

Inverted

reduced Real

Inverted

Enlarged

Virtual

Upright

Enlarged

At the focal point the image changes

from real to virtual

Question

How will an object viewed through a

converging lens appear as the lens is brought closer to the object?

Real Image

Inverted

Real Image

Inverted

Magnified

Virtual Image

Upright

Magnified

8

Virtual image

Upright

Parallel light though a diverging

lens appears to go through the focal point.

A virtual image is formed.

Image formed by a Diverging lens

Virtual

Upright

Reduced

A Diverging lens always forms a

virtual image

Question

How will the image of an object formed by a

diverging lens change as the lens is brought closer to the object?

Virtual Image

Upright

Reduced

9

Virtual image

Upright

Reduced

Virtual image

Upright

Reduced

Thin lens equation.

111
pqf p is positive for real objects f is positive for converging lenses f is negative for diverging lenses q is positive for real images q is negative for virtual images.p and q are positive if light passes through

Magnification

h' qMhp for real image q is positive - image is inverted for virtual image q is negative - image is uprightM positive- upright

M negative- inverted

Example

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