MAGNIFICATION
EQUATION
Magnification
The magnification M of an image is the ratio of the height of the image the height of the
object:
This number is a dimensionless ratio (a length over a length) and does not have any
units. To calculate M for virtual images, consider the diagram below:
From similar triangles:
Remember!
✔ +di = real image located in front of the mirror
✔ -di = virtual image located behind the mirror
✔ +hi = upright virtual image located behind the mirror
✔ -hi = inverted real image located in front of the mirror
✔ +f = Concave lens
✔ -f = Convex lens
✔ +M = Upright image ✔ -M = Inverted Image
✔ M greater than 1 = Image is LARGER than Object
✔ M between 0 & 1 = Image is SMALLER than Object
Magnification:
Magnification
This result also holds for real images:
Rule:
The magnification factor M of a lens
is always positive and given by:
From the diagram, using similar triangles:
Sample Problems
A concave mirror produces an inverted image that is magnified 2.5 fold. Determine the
image distance if the original object was placed 4.0 cm in front of the mirror.
Given:
Equation:
M = (-2.5)
do = 4.0 cm
Asked:
Image distance ?
Derive:
Substitute:
di = -(M x do)
di = - ( (-2.5) x 4.5 cm )
= 10 cm
Therefore, the image is
10 cm from the mirror.
Sample Problems
Determine the image height for a 5.00 cm tall object placed 45.0 cm from the concave
mirror if the image is real and is 22.5 cm from the mirror.
Given:
ho = 5.00 cm
do = 45.0 cm
Equation:
Derive:
Substitute:
hi = -(di x ho)/do
hi = -(22.5 cm x 5.00 cm)/45.0 cm
= -2.50 cm
di = 5.00 cm
Therefore, the height of the
Asked:
Image height ?
inverted image is 2.50 cm