CONCAVE VS. CONVEX MIRRORS
A concave mirror (figure A) is also known as a converging mirror because all of the
reflected rays come together (converge) at the focal point. Since the focus is in front of
the mirror, the focal length is positive when using the mirror equation.
A convex mirror (figure B) is also known as a diverging mirror because all of the reflected
rays spread apart (diverge). The focus is located behind the mirror because you can
extend the reflected rays behind the mirror. This is now known as a virtual focus. Since
the focus is behind the mirror, the focal length is negative when using the mirror equation.
Examples:
1. A 4.0 cm tall light bulb is placed at a distance of 35.5 cm from a convex mirror having a
focal length of 12.2 cm.
a) Calculate the image distance
b) Calculate the image height
G:
A: a)
f = - 12.2cm
ho = 4.0cm
R: di =?
b)
hi = ?
do = 35.5cm
S:
P: Therefore, the image distance is ____________ and the image height is __________
4. A object is placed 76.8 cm from a convex mirror. A virtual image is produced 18.63 cm
from the mirror. What is the magnification?
G:
do = 76.8cm
R: M = ?
A:
di = - 18.63cm
S:
P: Therefore, the magnification is _________.
Mirror and Magnification Equations for Convex Mirrors
The mirror and magnification equations that are used for concave mirrors are also used
for convex mirrors. The only difference is that since the focus is located behind the
mirror, the focal length for a convex mirror is negative.
Practice Questions:
1. A convex mirror has a focal length of -20.0cm. An object is placed at 10.0cm.
Determine the image distance.
2. A convex surveillance mirror in a convenience store has a focal length of -0.40 m.
A customer, who is 1.7 m tall, is standing 4.5 m in front of the mirror.
a) Calculate the image distance.
b) Calculate the image height.
3. A spherical, polished metallic ball is used as a diverging mirror, with a focal length
of 20.0cm, over a birdbath. A bird, 25.0cm tall, standing 50.0cm away, looks
directly at the mirror. What is the size and position of the bird’s image?
4. A convex security mirror has a focal length of 0.25 m. A person with a height of
1.5 m is 4.0 m from the mirror.
a) Calculate the image distance.
b) Calculate the image height.
5. An object 0.40m tall is placed 2.50m in front of a convex mirror that has a focal
length of 0.90m.
a) Calculate the image distance.
b) Calculate the image height.
6. A butterfly is 10.0cm from a diverging mirror and its image is 15.0cm behind the
mirror.
a) Calculate the focal length of the mirror.
b) Calculate the magnification of the image.