The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f) of a spherical mirror. It is applicable to both concave and convex mirrors, with the focal length being positive for concave mirrors and negative for convex mirrors. The distances of real images are positive and virtual images are negative. For a concave mirror with a focal length of 10 cm and an object placed 15 cm in front, the mirror equation is used to calculate that the image distance is 30 cm, indicating a real image is formed behind the mirror.

1. Subtitle

2. Mirror Equation
There is an important relationship between the
distance of an object, distance of an image, and the
focal length of the spherical mirror. This relationship is
known as the mirror equation. The mirror equation
expresses the quantitative relationship between the object
distance (do), the image distance (di), and the focal length
(f). In symbols,
𝟏
𝒇
=
𝟏
𝒅 𝒐
+
𝟏
𝒅𝒊

3. This mirror equation is both applicable to concave
and convex mirrors. In a concave mirror, the focal length
is positive (+) while in a convex mirror it is negative (-).
The distance of the object and the distance of the image
is taken as positive (+) because they are both located in
front of the mirror and taken as negative (-) for virtual
images because they are formed behind the mirror.

4. Example 1:
A flower vase is placed 15 cm in front of a concave
mirror whose focal length is 10 cm. Where is the image
of the flower vase located? Describe the image formed.
Given:
do = 15 cm
f = 10 cm
Solution:
Using the basic equation, derive the formula for
the distance of the image.

5. 𝟏
𝒇
=
𝟏
𝒅 𝒐
+
𝟏
𝒅𝒊
f do di
𝟏
𝒇
=
𝟏
𝒅 𝒐
+
𝟏
𝒅𝒊
f do di
do di = fdi + fdo
dodi – fdi = fdo
𝒅𝒊
(𝒅𝒐 − −𝒇)
𝒅 𝒐
−𝒇
=
𝒇 𝒅𝒐
(𝒅𝒐 − 𝒇)
di =
𝒇 𝒅𝒐
𝒅𝒐 − 𝒇
di =
𝒇 𝒅𝒐
(𝒅𝒐 − 𝒇)
di =
𝟏𝟎 𝒄𝒎 (𝟏𝟓 𝒄𝒎)
(𝟏𝟓 𝒄𝒎 −𝟏𝟎 𝒄𝒎)
di =
𝟏𝟓𝟎 𝒄𝒎 𝟐
𝟓𝒄𝒎
di = 30 cm