Mirrors

Recall: images formed by curved mirrors depend on position of image

Images could be: Real or virtual Upright or inverted Smaller or larger OR no image (if object at F)

Images – Concave Mirror

FCoh

ih

od

id

f

Images – Convex Mirror

F C

oh ih

od id

f

Sign Conventions: All distances are measured from

vertex: In front = positive Behind = negative

Focal length: Positive for concave mirrors Negative for convex mirrors

Distance: di & do positive if image & object are on

reflecting side of mirror (i.e. real) di & do negative if image or object is behind

the mirror (i.e. image virtual)

Sign Conventions:

Height: Positive for upright objects or images Negative for inverted objects or images

Magnification: Positive for upright images Negative for inverted images

Mirror Equation:

fdd io

111

Magnification:

o

i

o

i

dd

hhm

A 4cm tall object is located 30cm from a concave mirror with a focal length of 5cm. How tall is the image?

fdd io

111

511

301

id

cmdi 6

o

i

o

i

dd

hh

306

4i

h

cmhi 8.0

A convex mirror with a focal length of -5cm produces an image of an object located 15cm from the mirror. What is the magnification?

fdd io

111

511

151

id

cmdi 8.3

o

i

ddM

158.3

M

25.0M

A 1.5cm high diamond ring is placed 20cm in front of a concave mirror whose radius of curvature is 30cm. What is the size of the image?

fdd io

111

1511

201

id

cmdi 60

o

i

o

i

dd

hh

2060

5.1ih

cmhi 5.4

An object is placed 10m in front of a curved mirror. A virtual image is formed 19.6cm from the mirror. What type of mirror was used?

fdd io

111

f1

196.01

101

mf 2.0

Alex places a 5cm tall candle 30cm in front of a mirror that has a focal length of -50cm. What is the magnification?

fdd io

111

5011

301

id

cmdi 75.18

o

i

ddM

3075.18

M

625.0M

Matt is manipulating a concave mirror that has a focal length of 10cm. His physics teacher tells him that the difference between do & di if 15cm and that the image in larger than the object & has a negative magnification. Where should Matt place the object to obtain the desired image?A) do = 15cm & di = 30cmB) do = 30cm & di = 15cmC) do = 5cm & di = -10cmD) do = 10cm & di = -5cm