Physics - Mirror Problems
While a ray diagram may help one determine the approximate location and size of the image, it
will not provide numerical information about image distance and object size.
Mirror Equation
The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and
the focal length (f). The equation is stated as follows:
Magnification Equation
The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi)
and object height (ho). The magnification equation is stated as follows:
The +/- Sign Conventions
The sign conventions for the given quantities in the mirror equation and magnification equations are as follows:
• f is + if the mirror is a concave mirror
• f is - if the mirror is a convex mirror
• di is + if the image is a real image and located on the object's side of the mirror.
• di is - if the image is a virtual image and located behind the mirror.
• hi is + if the image is an upright image (and therefore, also virtual)
• hi is - if the image an inverted image (and therefore, also real)
Example Problem 1
A 4.0-cm tall light bulb is placed a distance of 8.3 cm from a concave mirror having a focal length of 15.2 cm. Determine
the image distance and the image size.
• Again, begin by the identification of the known information.
ho = 4.0 cm
do = 8.3 cm
f = 15.2 cm
•
Next identify the unknown quantities that you wish to solve for.
hi = ???
di = ???
•
To determine the image distance, the mirror equation will have to be used.
o 1/f = 1/do + 1/di
o 1/(15.2 cm) = 1/(8.3 cm) + 1/di
o 0.0658 cm-1 = 0.120 cm-1 + 1/di
o -0.0547 cm-1 = 1/di
o di = -18.3 cm
•
To determine the image height, the magnification equation is needed.
o hi/ho = - di/do
o hi /(4.0 cm) = - (-18.2 cm)/(8.3 cm)
o hi = - (4.0 cm) • (-18.2 cm)/(8.3 cm)
o hi = 8.8 cm
•
Determine the magnification of the image
o M = -di / do
o –(-18.3 cm) / (8.3 cm) =
o M = 2.2
Use the mirror equation and the magnification ratio to solve the following problems. Show Your Work.
1. Bobby places a 4.25-cm tall light bulb a distance of 36.2 cm from a concave mirror. If the mirror has a focal
length of 19.2 cm, then what is the image height and image distance?
2. Van Itee, quite concerned about the pimple on his chin, is looking into a concave mirror with a focal length of 33.6
cm. Determine the image height and image distance of the 2.50-mm (.25 cm) (sized pimple when placed 25.2 cm
from the mirror.
3. Al Wayscurious is intrigued by the reflective abilities of his family's soup ladle. The ladle acts as a concave mirror
with a 2.59-cm focal length. Determine the image size of Al's 24.8-cm tall face when placed 12.8 cm from the
ladle's surface.
4. Mr. H splurged when he bought his Yugo and ordered the side mirror option. The mirror has a focal length of
-88.4 cm (.884 m). What is the image height of a 4.59-meter tall truck when located 12.6 meters away from the
mirror?
5. A holiday tree ornament with an 8.64-cm diameter serves as a convex mirror surface. Determine the image size
and the image distance of a 4-foot (121.9 cm) tall child standing a distance of 2.65 meters away.
6. Determine the focal length and magnification of a curved mirror that produces an image that is 16.0 cm behind the
mirror when the object is 28.5 cm from the mirror. What type of curved mirror was used?
Curved Mirror Problem – Answer Key
Use the mirror equation and the magnification ratio to solve the following problems. PSYW
1.
Bobby places a 4.25-cm tall light bulb a distance of 36.2 cm from a concave mirror. If the mirror has a focal length of
19.2 cm, then what is the image height and image distance?
Given: ho = 4.25 cm
do = 36.2 cm
f = 19.2 cm
Find di and hi
di = 40.9 cm
hi/ho = -di/do  hi = -ho•di/do = -(4.25 cm)•(40.884705 … cm)/(36.2 cm) = -4.80 cm
2.
Van Itee, quite concerned about the pimple on his chin, is looking into a concave mirror with a focal length of 33.6
cm. Determine the image height and image distance of the 2.50-mm sized pimple when placed 25.2 cm from the
mirror.
Given: f = 33.6 cm
ho = 2.50 mm or .25 cm do = 25.2 cm
Find di and hi
di = -100.8 cm
hi/ho = -di/do  hi = -ho•di/do = -(2.50 mm)•(-100.8 cm)/(25.2 cm) = 10.00 mm or 1 cm
3.
Al Wayscurious is intrigued by the reflective abilities of his family's soup ladle. The ladle acts as a concave mirror
with a 2.59-cm focal length. Determine the image distance and size of Al's 24.8-cm tall face when placed 12.8 cm
from the ladle's surface.
Given: f = 2.59 cm
ho = 24.8 cm
do = 12.8 cm
Find hi
di = 3.247012 cm
hi/ho = -di/do  hi = -ho•di/do = -(24.8 cm)•(3.247012 … cm)/(12.8 cm) = -6.3 cm
4.
Mr. H splurged when he bought his Yugo and ordered the side mirror option. The mirror has a focal length of -88.4
cm. What is the image distance and height of a 4.59-meter tall truck when located 12.6 meters away from the mirror?
Given: f = -88.4 cm or -.884 m ho = 4.59 m
do = 12.6 m
Find hi
di = -82.60456 cm
hi/ho = -di/do  hi = -ho•di/do = -(4.59 m)•(-82.60456 … cm)/(12.6 m) = 30.1 cm
5.
A holiday tree ornament with an 8.64-cm diameter serves as a convex mirror surface. Determine the image size and
the image distance of a 4-foot tall child standing a distance of 2.65 meters away.
Given: diameter = 8.64 cm  R = -4.32 cm  f = -2.16 cm ho = 4.00 ft or 121.9 cm do = 2.65 m or 265 cm
Find di and hi
di = -2.14 … cm
hi/ho = -di/do  hi = -ho•di/do = 0.0323 ft or .98 cm
6. Determine the focal length and magnification of a curved mirror that produces an image that is 16.0 cm behind the
mirror when the object is 28.5 cm from the mirror. What type of curved mirror was used?
Use the equation 1 / f = 1 / do + 1 / di where do = 28.5 cm and di = -16.0 cm
Answer: f = -36.6 cm
Image distances for convex mirrors are always negative.
Magnification = .56