Chapter 23Chapter 23Mirrors and LensesMirrors and Lenses

Conceptual questions: 4,5,10,14,15,17

Quick Quizzes: 1,2,4,6

Problems: 17,44,53,61

Types of Images for Mirrors Types of Images for Mirrors and Lensesand Lenses

A A real imagereal image is one in which light is one in which light actually passes through the image actually passes through the image pointpoint Real images can be displayed on Real images can be displayed on

screensscreens A A virtualvirtual imageimage is one in which the is one in which the

light does not pass through the light does not pass through the image pointimage point Virtual images cannot be displayed on Virtual images cannot be displayed on

screensscreens

Flat MirrorFlat MirrorThe The object distanceobject distance is is the distance from the the distance from the object to the mirror or object to the mirror or lenslens

Denoted by Denoted by pp

The The image distanceimage distance is is the distance from the the distance from the image to the mirror or image to the mirror or lenslens

Denoted by Denoted by qq

The The lateral lateral magnificationmagnification of the of the mirror or lens is the mirror or lens is the ratio of the image ratio of the image height to the object height to the object heightheight

Denoted by Denoted by MM

In the overhead view of the figure below, the image of the stone seen by observer 1 is at C. Where does observer 2 see the image––at A, at B, at C, at D, at E, or not at all?

QUICK QUIZ 23.1

Day and Night Settings on Day and Night Settings on Auto MirrorsAuto Mirrors

Concave Concave MirrorMirror

The mirror has a The mirror has a radius radius of curvatureof curvature of R of R

Its Its center of curvaturecenter of curvature is the point Cis the point C

Point V is the center of Point V is the center of the spherical segmentthe spherical segment

A line drawn from C to A line drawn from C to V is called the V is called the principle principle axisaxis of the mirror of the mirror

Image Formed by a Concave Image Formed by a Concave MirrorMirror

Geometry shows Geometry shows the relationship the relationship between the between the image and object image and object distance isdistance is

Magnification isMagnification is

R

2

q

1

p

1

p

q

h

'hM

h’ is negative when the image is inverted with respect to the objecth’ is negative when the image is inverted with respect to the object

Focal Length Shown by Focal Length Shown by Parallel RaysParallel Rays

Focal LengthFocal Length Focal length, the Focal length, the

distance between distance between the focal point the focal point and the mirror, is and the mirror, is half the radiushalf the radius

The mirror The mirror equation can be equation can be expressed asexpressed as

f = R / 2f = R / 2

f

1

q

1

p

1

Convex MirrorsConvex MirrorsA convex mirror is also called a A convex mirror is also called a diverging diverging mirrormirror

Ray DiagramRay Diagram

Ray 1 is drawn parallel to the Ray 1 is drawn parallel to the principle axis and is reflected back principle axis and is reflected back through the focal point, Fthrough the focal point, F

Ray 2 is drawn through the focal Ray 2 is drawn through the focal point and is reflected parallel to point and is reflected parallel to the principle axisthe principle axis

Ray 3 is drawn through the center Ray 3 is drawn through the center of curvature and is reflected back of curvature and is reflected back on itselfon itself

Ray Diagram for Concave Ray Diagram for Concave Mirror, p > RMirror, p > R

Draw a ray diagram forDraw a ray diagram fora. a convex mirrora. a convex mirrorb. a concave mirror with b. a concave mirror with the object at a distance the object at a distance p>Rp>R

Based on conceptual question 17

Ray Diagram for a Convex Ray Diagram for a Convex MirrorMirror

Ray Diagram for a Ray Diagram for a Concave Mirror, p < fConcave Mirror, p < f

True or false?

(a) The image of an object placed in front of a concave mirror is always upright. (b) The height of the image of an object placed in front of a concave mirror must be smaller than or equal to the height of the object. (c) The image of an object placed in front of a convex mirror is always upright and smaller than the object.

Problem 17Problem 17

A child holds a candy bar 10.0 cm A child holds a candy bar 10.0 cm in front of a convex mirror and in front of a convex mirror and notices that the image is only one-notices that the image is only one-half the size of the candy bar. half the size of the candy bar. What is the radius of curvature of What is the radius of curvature of the mirror?the mirror?

Images Formed by Images Formed by RefractionRefraction

When nWhen n22 > n > n11,, Object distance, image distance and radius of curvature are related by the equation:

Real images are formed on the side Real images are formed on the side opposite from the objectopposite from the object

Sign conventions – Table 23.2Sign conventions – Table 23.2pn

qn

h

'hM

2

1

1 2 2 1n n n n

p q R

Sign convention for Sign convention for refracting surfacesrefracting surfaces

Flat Refracting SurfaceFlat Refracting Surface

The image and the The image and the object are on the object are on the samesame side of the surface. side of the surface. The image is The image is virtualvirtual

QUICK QUIZ 23.2

A person spear fishing from a boat sees a fish located 3 m from the boat at an apparent depth of 1 m. To spear the fish, should the person aim

(a) at, (b) above, or (c) below the image of the fish?

Problem 53Problem 53

A parallel beam of light enters a glass A parallel beam of light enters a glass hemisphere perpendicular to the flat hemisphere perpendicular to the flat face, as shown in Figure P23.53. The face, as shown in Figure P23.53. The radius is radius is R R = 6.00 cm, and the index = 6.00 cm, and the index of refraction is of refraction is n n = 1.560. Determine = 1.560. Determine the point at which the beam is the point at which the beam is focused. (Assume paraxial rays; that focused. (Assume paraxial rays; that is, all rays are located close to the is, all rays are located close to the principal axis.)principal axis.)

Conceptual questionConceptual question

10. Why does a clear stream 10. Why does a clear stream appear to be shallower than it appear to be shallower than it actually is?actually is?

Atmospheric Refraction Atmospheric Refraction and Miragesand Mirages A mirage can be observed A mirage can be observed

when the air above the when the air above the ground is warmer than the ground is warmer than the air at higher elevationsair at higher elevations

The rays in path B are The rays in path B are directed toward the directed toward the ground and then bent by ground and then bent by refractionrefraction

The observer sees both an The observer sees both an upright and an inverted upright and an inverted imageimage

Thin Lens ShapesThin Lens Shapes These are examples These are examples

of of convergingconverging lenses lenses They have positive They have positive

focal lengthsfocal lengths They are thickest in They are thickest in

the middlethe middle

Thin Diverging LensesThin Diverging Lenses These are examples These are examples

of of divergingdiverging lenses lenses They have negative They have negative

focal lengthsfocal lengths They are thickest at They are thickest at

the edgesthe edges

Lens EquationsLens Equations

The geometric The geometric derivation of the derivation of the equations is very equations is very similar to that of similar to that of mirrorsmirrors

f

1

q

1

p

1

p

q

h

'hM

Sign Conventions for Thin Sign Conventions for Thin LensesLenses

QuantityQuantity Positive Positive WhenWhen

Negative Negative WhenWhen

Object location (p)Object location (p) Object is in front of Object is in front of the lensthe lens

Object is in back of Object is in back of the lensthe lens

Image location (q)Image location (q) Image is in back of Image is in back of the lensthe lens

Image is in front of Image is in front of the lensthe lens

Image height (h’)Image height (h’) Image is uprightImage is upright Image is invertedImage is inverted

RR11 and R and R22 Center of curvature Center of curvature is in back of the is in back of the lenslens

Center of curvature Center of curvature is in front of the is in front of the lenslens

Focal length (f)Focal length (f) Converging lensConverging lens Diverging lensDiverging lens

The Lens Maker’s formulaeThe Lens Maker’s formulae

21 R

1

R

1)1n(

f

1

Ray Diagrams for Thin Ray Diagrams for Thin LensesLenses

The first ray is drawn parallel to the first The first ray is drawn parallel to the first principle axis and then passes through (or principle axis and then passes through (or appears to come from) one of the focal appears to come from) one of the focal lengthslengths

The second ray is drawn through the The second ray is drawn through the center of the lens and continues in a center of the lens and continues in a straight linestraight line

The third ray is drawn from the other focal The third ray is drawn from the other focal point and emerges from the lens parallel point and emerges from the lens parallel to the principle axisto the principle axis

Ray Diagram for Ray Diagram for Converging Lens, p > fConverging Lens, p > f

The image is realThe image is real The image is invertedThe image is inverted

Ray Diagram for Ray Diagram for Converging Lens, p < fConverging Lens, p < f

The image is virtualThe image is virtual The image is uprightThe image is upright

Ray Diagram for Diverging Ray Diagram for Diverging LensLens

The image is virtualThe image is virtual The image is uprightThe image is upright

Conceptual questionsConceptual questions

5. You are taking a picture of yourself 5. You are taking a picture of yourself with a camera that uses an ultrasonic with a camera that uses an ultrasonic range finder to measure the distance to range finder to measure the distance to the object. When you take a picture of the object. When you take a picture of yourself in a mirror with this camera, yourself in a mirror with this camera, your image is out of focus. Why?your image is out of focus. Why?

14. Lenses used in sunglasses whether 14. Lenses used in sunglasses whether converging or diverging, are always converging or diverging, are always designed such that the middle of the designed such that the middle of the lens curves away from the eye. Why?lens curves away from the eye. Why?

A plastic sandwich bag filled with water can act as a crude converging lens in air. If the bag is filled with air and placed under water, is the effective lens (a) converging or (b) diverging?

QUICK QUIZ 23.4

An object is placed to the left of a converging lens. Which of the following statements are true and which are false? (a) The image is always to the right of the lens. (b) The image can be upright or inverted. (c) The image is always smaller or the same size as the object.

QUICK QUIZ 23.6

Combination of Thin Combination of Thin Lenses, exampleLenses, example

Problem 44. Problem 44. Two converging lenses having Two converging lenses having focal lengths of 10.0 cm and 20.0 cm are focal lengths of 10.0 cm and 20.0 cm are placed 50.0 cm apart, as shown in Figure. The placed 50.0 cm apart, as shown in Figure. The final image is to be located between the lenses, final image is to be located between the lenses, at the position indicated. (a) How far to the left at the position indicated. (a) How far to the left of the first lens should the object be of the first lens should the object be positioned? (b) What is the overall positioned? (b) What is the overall magnification? (c) Is the final image upright or magnification? (c) Is the final image upright or inverted?inverted?

Problem 61Problem 61 The lens maker’s equation for a lens with The lens maker’s equation for a lens with

index index nn11 immersed in a medium with index immersed in a medium with index nn22 takes the form takes the form

1/f=(n1/f=(n11/n/n22-1)(1/R-1)(1/R11-1/R-1/R22)) A thin diverging glass lens (index = 1.50) A thin diverging glass lens (index = 1.50)

with with RR11 = –3.00 m and = –3.00 m and RR22 = –6.00 m is = –6.00 m is surrounded by air. An arrow is placed 10.0 surrounded by air. An arrow is placed 10.0 m to the left of the lens. m to the left of the lens.

(a)(a) Determine the position of the image. Determine the position of the image. (b)(b) Repeat with the arrow and lens immersed in Repeat with the arrow and lens immersed in

water (index = 1.33); water (index = 1.33); (c)(c) a medium with an index of refraction of a medium with an index of refraction of

2.00. 2.00.

Spherical AberrationSpherical Aberration

Results from the focal Results from the focal points of light rays points of light rays far from the principle far from the principle axis are different axis are different from the focal points from the focal points of rays passing near of rays passing near the axisthe axis

For a mirror, For a mirror, parabolic shapes can parabolic shapes can be used to correct for be used to correct for spherical aberrationspherical aberration

Chromatic AberrationChromatic Aberration Different wavelengths of Different wavelengths of

light refracted by by a light refracted by by a lens focus at different lens focus at different pointspoints Violet rays are refracted Violet rays are refracted

more than red raysmore than red rays The focal length for red The focal length for red

light is greater than the light is greater than the focal length for violet lightfocal length for violet light

Chromatic aberration Chromatic aberration can be minimized by the can be minimized by the use of a combination of use of a combination of converging and converging and diverging lensesdiverging lenses

Question 4. Explain why a mirror cannot Question 4. Explain why a mirror cannot give rise to chromatic aberration.give rise to chromatic aberration.

Question 15. Why does a focal length of a Question 15. Why does a focal length of a mirror not depend on the mirror material mirror not depend on the mirror material when the focal length of a lens depends when the focal length of a lens depends on the lens material?on the lens material?

Conceptual questions

True or false?

(a) The image of an object placed in front of a concave mirror is always upright. (b) The height of the image of an object placed in front of a concave mirror must be smaller than or equal to the height of the object. (c) The image of an object placed in front of a convex mirror is always upright and smaller than the object.

Review questionsReview questions1.1. What is the focal length of a flat mirror?What is the focal length of a flat mirror?a.a. 00b.b. positivepositivec.c. infiniteinfinited.d. NegativeNegative

2. The magnification of a 3 cm object placed 2. The magnification of a 3 cm object placed 5 cm from a certain lens is -1. What is the 5 cm from a certain lens is -1. What is the focal distance of the lens?focal distance of the lens?

a.a. 0.4 cm0.4 cmb.b. 0.5 cm0.5 cmc.c. 2.5 cm2.5 cmd.d. 5.0 cm5.0 cm

3.3. Which of the following is responsible for Which of the following is responsible for mirage?mirage?

a. diffractiona. diffraction

b. reflectionb. reflection

c. refractionc. refraction

d. dispersiond. dispersion

4. An alligator sits 1 m below the surface of 4. An alligator sits 1 m below the surface of water of index of refraction n=1.4. The water of index of refraction n=1.4. The alligator’s view of objects above the surface alligator’s view of objects above the surface is restricted to a circular window at the is restricted to a circular window at the surface of radiussurface of radiusa. 0.5 ma. 0.5 m b.b. 1 m1 m

c.c. 2 m 2 m d.d. 2.6 m2.6 m