The Mirror Equation
The mirror equation relates the object distance (u), image distance (v), and focal length (f) of a spherical mirror:
1/v + 1/u = 1/f
or
v = (u × f)/(u - f)
The magnification (m) of the mirror is given by:
m = -v/u
Sign Convention:
- All distances are measured from the pole of the mirror
- Object distance (u) is always negative
- For real images, image distance (v) is positive
- For virtual images, image distance (v) is negative
- For concave mirrors, focal length (f) is positive
- For convex mirrors, focal length (f) is negative
Mirror Type
Object Distance (u)
NearFar
u = 150 units
Focal Length (f)
SmallLarge
f = +100 units
Calculated Results
Negative value means virtual image (behind mirror)
Negative value means inverted image
Magnification < 1 means image is smaller than object
Image Type: Virtual
Image Orientation: Inverted
Image Size: Diminished
Everyday Example:
Concave mirrors are used in makeup mirrors and shaving mirrors. When your face is close to the mirror (less than the focal length), you see an enlarged, upright, virtual image of yourself.