14-3: Curved Mirrors

Curved Mirrors

• What are some examples of curved mirrors?

Concave Spherical Mirrors

• A spherical mirror has the shape of part of a sphere’s surface.

• Concave Spherical Mirror (Converging Mirror): A spherical mirror with light reflecting from its silvered, concave surface– Concave mirrors are used whenever a magnified

image of an object is needed

Terms you need to knowTerm Definition Symbol(s)

Center of Curvature The center of the spherical shell of which the mirror is a small part

C

Radius of Curvature The distance from the mirror’s surface to the center of curvature

R

Height of object The height of the object h; ho

Height of image The height of the image h’, hi

Object distance The distance between the object and the mirror

p; do

Image distance The distance between the image and the mirror

q; di

Focal Length Focal length is equal to half the radius of curvature

f

Concave Spherical Mirrors (p.531)

Object

Principal Axis C f

A spherical mirror is represented as a shell of a sphere

Concave Mirror (p.531)

The Mirror Equation

fqp

111

length focal

1

distance image

1

distanceobject

1

•To use the mirror equation, you must use the correct signs.

•Object and image distances are positive if they form on the front side of the mirror

•Object and image distances are negative if they form on the back side of the mirror

Sample Problem (p.536 #2)

• A concave shaving mirror has a focal length of 33 cm. Calculate the image position of a cologne bottle placed in front of the mirror at a distance of 93 cm.

Solve the problem

fqp

111

• p = .93 m• f = .33 m• q=?

01955.93.

1

33.

1111

mmpfq

51.15cmm 51. q

Magnification Equation

distanceobject

distance image

heightobject

height imageonagnificati M

p

qM

o

i

h

h

Sample Problem (p.536 #2)

• A concave shaving mirror has a focal length of 33 cm. Calculate the magnification of the image. Is the image real or virtual? Is the image inverted or upright?

Sign Conventions for Magnification

Orientation of image with respect to object

Sign of M Type of image

Upright + Virtual

Inverted - Real

Find the magnification

55.93.

51.

h

h

o

i p

qM

The magnification is negative, therefore the image is real and inverted.

Ray Diagrams

• A ray diagram is a drawing that uses geometry to locate an image formed by a mirror.

• There are different rules for drawing ray diagrams depending on the type of mirror you have.

How to draw a ray diagram (p. 533-534)

• For spherical mirrors, there are three different reference rays.

• The intersection of any two rays locates the image

Rules for drawing reference rays (p. 534)

Ray Line drawn from object to mirror Line drawn from mirror to image after reflection

1 Parallel to principal axis Through focal point F

2 Through focal point F Parallel to principal axis

3 Through center of curvature (C)

Back along itself through C

How to draw a ray diagram

Ray 1

Ray 2

fC

Ray 3The intersectionOf any 2 rays gives the image location

Objects inside the focal point

fC

Sample Problem (p.536 #2)

• A concave shaving mirror has a focal length of 33 cm. Calculate the image position of a cologne bottle placed in front of the mirror at a distance of 93 cm. Draw a ray diagram to confirm your results.

Draw the diagram

fC

The image is inverted and about half the height of the object.

Convex Mirrors

• Convex mirrors take objects in a large field of view and produce a small image– Side-view mirrors on cars are convex mirrors.

That’s why they say “objects are closer than they appear”

Convex Spherical Mirrors (p. 537)

• A convex spherical mirror (diverging mirror) is silvered so that light is reflected from the sphere’s outer, convex surface– The image distance is always negative!– The image is always a virtual image!– The focal length is negative !

Ray diagrams for convex mirrors

• The focal point and center of curvature are behind the mirror’s surface – A virtual, upright image is formed behind the mirror– The magnification is always less than 1

f C

Drawing the reference rays

• Ray 1 is drawn parallel to the principal axis beginning at the top of the object. It reflects from the mirror along a line that intersects the focal point

f C

Ray 2

• Ray 2 starts from the top of the object and goes as though its going to intersect the focal point but it reflects parallel to the principal axis

Ray 1

f C

Ray 2

Ray 3

• Ray 3 starts at the top of the object and goes as though its going to intersect the center of curvature

Ray 1

f C

Ray 2

Ray 3

Convex Spherical Image Formation

• The image forms at the intersection of any two of the three rays behind the mirror.

Ray 1

f C

Ray 2

Ray 3

The rays do not intersect in front of the mirror!!

Sign conventions for mirrors (p. 538)

Sample Problem (p. 540 #6)

• A candle is 49 cm in front of a convex spherical mirror that has a focal length of 35 cm. What are the image distance and magnification? Is the image virtual or real? Is the image inverted or upright? Draw a ray diagram to confirm your results.

Solving the problem

• Remember that for convex mirrors, the focal length and image distance are always negative.

fqp

111

cmpfq

049.49

1

35

1111

mirror thebehind cm 20.42 is image The ;42.20 cmq

The Magnification of the Image

• Since the magnification is positive, the image is upright and virtual

42.49

42.20

p

qM

Ray diagram for the Image

f C

Remember that you only need to draw two of the three rays to find the image.