Reflection and Mirrors

• Explain and discuss with diagrams, reflection, absorption, and refraction of light rays.

• Define and illustrate your understanding of real, virtual, erect, inverted, enlarged, and diminished as applied to images. • Use geometrical optics to draw images of an object at various distances from converging and diverging mirrors.

• Illustrate graphically the reflection of light from plane, convex, and concave mirrors.

Geometrical Optics

In the study of how light behaves, it is useful to use “light rays” and the fact that light travels in straight lines.

In the study of how light behaves, it is useful to use “light rays” and the fact that light travels in straight lines.

When light strikes the boundary between two media, three things may happen: reflection, refraction, or absorption.

reflection

refraction

absorption

Water

Air

Reflection, Refraction, and Absorption

Water

AirReflection:Reflection: A A ray from air ray from air strikes the strikes the water and water and returns to the returns to the air.air.Refraction:Refraction: A A ray bends into ray bends into the water the water toward the toward the normal line.normal line.

Absorption:Absorption: A ray A ray is absorbed is absorbed atomically by the atomically by the water and does water and does not reappear.not reappear.

reflection

refraction

absorption

Water

Air reflection

refraction

absorption

The Laws of Reflection

Water

Air1. The angle of 1. The angle of inci- dence inci- dence iiis is equal to the equal to the angle of angle of reflection reflection rr::i = r

i = r

i

N reflectionr

All ray angles are measured with respect to All ray angles are measured with respect to normal normal NN..2. The incident ray, 2. The incident ray,

the reflected ray, the reflected ray, and the normal and the normal NN all lie in the same all lie in the same plane.plane.

3. The rays 3. The rays are are completelcompletely y reversible.reversible.

The Plane Mirror

A A mirrormirror is a highly polished surface is a highly polished surface that forms images by uniformly that forms images by uniformly reflected light.reflected light.Note: images appear to be equi-distant behind mirror and are right-left reversed.

DefinitionsObject distance:Object distance: The straight-line The straight-line distance distance pp from the surface of a mirror from the surface of a mirror to the object. to the object. Image distance:Image distance: The straight-line The straight-line distance distance qq from the surface of a mirror from the surface of a mirror to the image. to the image.

Object distanc

e

Image distanc

e

=

p = q

i = r

ObjecObjectt

ImageImage

pp qq

Real and VirtualReal imagesReal images and and objects are formed objects are formed by actual rays of by actual rays of light. (Real images light. (Real images can be projected can be projected on a screen.)on a screen.)

Virtual imagesVirtual images and and objects do not objects do not really exist, but really exist, but only seem to be at only seem to be at a location.a location.

Virtual images are on Virtual images are on the the oppositeopposite side of the side of the mirror from the mirror from the incoming rays.incoming rays.

Real object

Virtual image

Light rays

No light

Image of a Point ObjectPlane mirror

Real object

p

Image appears to be at same Image appears to be at same distance behind mirror regardless of distance behind mirror regardless of viewing angle.viewing angle.

Image appears to be at same Image appears to be at same distance behind mirror regardless of distance behind mirror regardless of viewing angle.viewing angle.

qVirtual image

q = p

Image of an Extended Object

Plane mirror

p q

Image of bottom and top of guitar Image of bottom and top of guitar shows forward-back, right-left shows forward-back, right-left reversals.reversals.

Image of bottom and top of guitar Image of bottom and top of guitar shows forward-back, right-left shows forward-back, right-left reversals.reversals.

q = p

Virtual image

Terms for Spherical MirrorsA A spherical mirrorspherical mirror is formed by the is formed by the inside (inside (concaveconcave) ) or outside or outside ((convexconvex) surfaces ) surfaces of a sphere.of a sphere.A A concave concave spherical mirrorspherical mirror is is shown here with shown here with parts identified.parts identified.

Concave Mirror

Radius of curvature RVertex V

Center of Curvature CThe The axisaxis and and linear linear

apertureaperture are are shown.shown.

Linear aperture

V

C

R Axis

The Focal Length f of a Mirror

axis

r

i

R

Incident parallel ray

f

The focal length, f

The focal The focal length length f f is: is:

2

Rf

The focal length f is equal to half the radius RThe focal length f is equal to half the radius R

Since Since ii = = rr, we , we find that find that FF is is mid- way mid- way between between VV and and CC; we find:; we find:

C VF

Focal point

For objects lo- For objects lo- cated at cated at infinityinfinity, the , the realreal image image appears at the appears at the focal pointfocal point since rays of since rays of light are light are almost almost parallel.parallel.

For objects lo- For objects lo- cated at cated at infinityinfinity, the , the realreal image image appears at the appears at the focal pointfocal point since rays of since rays of light are light are almost almost parallel.parallel.

The Focus of a Concave MirrorThe focal point The focal point FF for a concave mirror is the for a concave mirror is the point at which all parallel light rays point at which all parallel light rays convergeconverge..

axis

Incident parallel Rays

CF

Focal Focal pointpoint

2

Rf

The Focus of a Convex MirrorThe The focal pointfocal point for a convex mirror is the for a convex mirror is the point point F F from which all parallel light rays from which all parallel light rays divergediverge..

axisC F

RR

Incident Rays

Reflected Rays

Virtual focus; reflected rays diverge.

2

Rf

Image Construction:

Ray 1:Ray 1: A ray parallel to mirror axis A ray parallel to mirror axis passes through the focal point of a passes through the focal point of a concave mirror or appears to come concave mirror or appears to come from the focal point of a convex mirror.from the focal point of a convex mirror.

Ray 1:Ray 1: A ray parallel to mirror axis A ray parallel to mirror axis passes through the focal point of a passes through the focal point of a concave mirror or appears to come concave mirror or appears to come from the focal point of a convex mirror.from the focal point of a convex mirror.

C F

Convex mirror

Object

C F

Concave mirror

Object

Ray 1

Ray 1

Image Construction (Cont.):

Ray 2:Ray 2: A ray passing through the focus A ray passing through the focus of a concave mirror or proceeding of a concave mirror or proceeding toward the focus of a convex mirror is toward the focus of a convex mirror is reflected parallel to the mirror axis. reflected parallel to the mirror axis.

Ray 2:Ray 2: A ray passing through the focus A ray passing through the focus of a concave mirror or proceeding of a concave mirror or proceeding toward the focus of a convex mirror is toward the focus of a convex mirror is reflected parallel to the mirror axis. reflected parallel to the mirror axis.

Concave mirror

C FRay 2

Ray 1

Image C F

Convex mirror Ray

2

Ray 1

Image

Image Construction (Cont.):

Ray 3:Ray 3: A ray that proceeds along a A ray that proceeds along a radius is always reflected back along its radius is always reflected back along its original path. original path.

Ray 3:Ray 3: A ray that proceeds along a A ray that proceeds along a radius is always reflected back along its radius is always reflected back along its original path. original path.

C F

Convex mirror

Concave mirror

C F

Ray 2

Ray 1

Ray 3

Ray 3

C F

Ray 2

Ray 1

Image

The Nature of ImagesAn object is placed in front of a concave An object is placed in front of a concave mirror. It is useful to trace the images as mirror. It is useful to trace the images as the object moves ever closer to the vertex the object moves ever closer to the vertex of the mirror.of the mirror.

An object is placed in front of a concave An object is placed in front of a concave mirror. It is useful to trace the images as mirror. It is useful to trace the images as the object moves ever closer to the vertex the object moves ever closer to the vertex of the mirror.of the mirror.We will want to locate the image and answer three questions for the possible positions:

3. Is it enlarged, diminished, or the same size?

2. Is the image real or virtual?

1. Is the image erect or inverted?

Object Outside Center C

Concave mirror

C FRay 3

Ray 2

Ray 1

1. The image is 1. The image is invertedinverted; i.e., ; i.e., opposite of the opposite of the object orientation.object orientation.

2. The image is 2. The image is realreal; ; i.e., formed by i.e., formed by actual light rays in actual light rays in front of mirror. front of mirror.

3. The image is 3. The image is diminished diminished in size; in size; i.e., smaller than the i.e., smaller than the object.object.

Image is located between C and F

Image is located between C and F

Object at the Center C

C F

Ray 2

Ray 1

1. The image is 1. The image is invertedinverted; i.e., ; i.e., opposite of the opposite of the object orientation.object orientation.

2. The image is 2. The image is realreal; ; i.e., formed by i.e., formed by actual light rays in actual light rays in front of mirror. front of mirror.

3. The image is 3. The image is the the same size same size as the as the object.object.

Image is located at C, inverted.

Image is located at C, inverted.

Ray 3

Object Between C and F1. The image is 1. The image is

invertedinverted; i.e., ; i.e., opposite of the opposite of the object orientation.object orientation.

2. The image is 2. The image is realreal; ; i.e., formed by i.e., formed by actual light rays in actual light rays in front of mirror. front of mirror.

3. The image is 3. The image is enlarged enlarged in size; i.e., in size; i.e., larger than the larger than the object.object.

Image is outside of the center C

Image is outside of the center C

CF

Ray 1

Ray 3

Ray 2

Object at Focal Point

Image is located at infinity (not formed).

Image is located at infinity (not formed).

C

F

Ray 3

Reflected rays are parallel

When the object When the object is located at the is located at the focal point of the focal point of the mirror, the image mirror, the image is is not formednot formed (or (or it is located at it is located at infinity).infinity).

When the object When the object is located at the is located at the focal point of the focal point of the mirror, the image mirror, the image is is not formednot formed (or (or it is located at it is located at infinity).infinity).

The parallel reflected The parallel reflected rays never cross.rays never cross.

Ray 1

Object Inside Focal Point1. The image is 1. The image is erecterect; ;

i.e., same i.e., same orientation as the orientation as the object.object.

2. The image is 2. The image is virtualvirtual; that is, it ; that is, it seems to be seems to be located located behindbehind mirror.mirror.3. The image is 3. The image is enlarged; enlarged; bigger bigger than the object.than the object.

Image is located behind the mirror

Image is located behind the mirror

C

FErect and enlarged

Virtual image

Observe the Images as Object Moves Closer to Mirror

Concave mirror

C FRay 3

Ray 2

Ray 1

C F

Ray 2

Ray 1

Ray 3

CF

Ray 1

Ray 3

Ray 2

C

F

Ray 3

Reflected rays are parallel

Ray 1

C

FErect and enlarged

Virtual image

Convex Mirror Imaging

C F

Convex mirror Ray

2

Ray 1

Image

All images are All images are erecterect, , virtualvirtual, and , and diminisheddiminished. Images get larger as object . Images get larger as object

approaches.approaches.

All images are All images are erecterect, , virtualvirtual, and , and diminisheddiminished. Images get larger as object . Images get larger as object

approaches.approaches.

C F

Convex mirror

Ray 1

2

Image gets larger as object

gets closer

Converging and Diverging MirrorsConcave Concave mirrors and mirrors and converging parallel rays converging parallel rays will be called will be called converging converging mirrorsmirrors from this point from this point onward.onward.

ConvexConvex mirrors and mirrors and diverging parallel rays diverging parallel rays will be called will be called diverging diverging mirrorsmirrors from this point from this point onward.onward.

CF

Converging Mirror

Concave

C F

Diverging Mirror

Convex

SummaryReflection:Reflection: A A ray from air ray from air strikes the strikes the water and water and returns to the returns to the air.air.

Refraction:Refraction: A A ray bends into ray bends into the water the water toward the toward the normal line.normal line.

Absorption:Absorption: A ray A ray is absorbed is absorbed atomically by the atomically by the water and does water and does not reappear.not reappear.

Water

Air reflection

refraction

absorption

Summary (Cont.)

Water

Air1. The angle of 1. The angle of inci- dence inci- dence iiis is equal to the equal to the angle of angle of reflection reflection rr::i = r

i = r

i

N reflectionr

All ray angles are measured with respect to All ray angles are measured with respect to normal normal NN..2. The incident ray, 2. The incident ray,

the reflected ray, the reflected ray, and the normal and the normal NN all lie in the same all lie in the same plane.plane.

3. The rays 3. The rays are are completelcompletely y reversible.reversible.

Summary (Definitions)Object distance:Object distance: The straight-line The straight-line distance distance pp from the surface of a mirror from the surface of a mirror to the object. to the object. Image distance:Image distance: The straight-line The straight-line distance distance qq from the surface of a mirror from the surface of a mirror to the image.to the image.Real image:Real image: An image formed by real An image formed by real light rays that can be projected on a light rays that can be projected on a screen. screen. Virtual image:Virtual image: An image that appears to An image that appears to be at a location where no light rays be at a location where no light rays reach. reach. Converging and diverging mirrors:Converging and diverging mirrors: Refer to Refer to the reflection of parallel rays from surface the reflection of parallel rays from surface of mirror.of mirror.

Image Construction Summary:

Ray 1:Ray 1: A ray parallel to mirror axis A ray parallel to mirror axis passes through the focal point of a passes through the focal point of a concave mirror or appears to come concave mirror or appears to come from the focal point of a convex mirror.from the focal point of a convex mirror.

Ray 1:Ray 1: A ray parallel to mirror axis A ray parallel to mirror axis passes through the focal point of a passes through the focal point of a concave mirror or appears to come concave mirror or appears to come from the focal point of a convex mirror.from the focal point of a convex mirror.

Ray 2:Ray 2: A ray passing through the focus A ray passing through the focus of a concave mirror or proceeding of a concave mirror or proceeding toward the focus of a convex mirror is toward the focus of a convex mirror is reflected parallel to mirror axis. reflected parallel to mirror axis.

Ray 2:Ray 2: A ray passing through the focus A ray passing through the focus of a concave mirror or proceeding of a concave mirror or proceeding toward the focus of a convex mirror is toward the focus of a convex mirror is reflected parallel to mirror axis. reflected parallel to mirror axis.

Ray 3:Ray 3: A ray that proceeds along a A ray that proceeds along a radius is always reflected back along its radius is always reflected back along its original path. original path.

Ray 3:Ray 3: A ray that proceeds along a A ray that proceeds along a radius is always reflected back along its radius is always reflected back along its original path. original path.

Summary (Cont.)For plane mirrors, the object distance For plane mirrors, the object distance equals the image distance and all images equals the image distance and all images are erect and virtual.are erect and virtual.

For converging mirrors and diverging For converging mirrors and diverging mirrors, the focal length is equal to one-mirrors, the focal length is equal to one-half the radius.half the radius.All images formed from convex mirrors All images formed from convex mirrors are erect, virtual, and diminished in size.are erect, virtual, and diminished in size.

Except for objects located inside the focus Except for objects located inside the focus (which are erect and virtual), all images (which are erect and virtual), all images formed by converging mirrors are real and formed by converging mirrors are real and inverted. inverted.