A shopper stands 0.6 m in front of a diverging mirror of focal length 0.2 m. Where is the image located and what is the magnification?
To determine the location and magnification of the image formed by a diverging mirror, you can use the mirror equation and the magnification formula.
1. Mirror equation:
The mirror equation relates the object distance (denoted as "do"), the image distance (denoted as "di"), and the focal length of the mirror (denoted as "f") by the equation:
1/do + 1/di = 1/f
2. Magnification formula:
The magnification (denoted as "m") of an image formed by a mirror is given by the formula:
m = -di/do
Now let's apply these formulas to solve the problem.
Given:
Object distance (do) = 0.6 m (positive because it is in front of the mirror)
Focal length (f) = -0.2 m (negative because it is a diverging mirror)
Step 1: Calculate the image distance (di) using the mirror equation.
Substituting the given values into the mirror equation:
1/0.6 + 1/di = 1/-0.2
Simplifying the equation:
5/3 + 1/di = -5
By rearranging the equation, we get:
1/di = -5 - 5/3
1/di = -20/3
Inverting both sides of the equation, we get:
di/1 = -3/20
Simplifying further, we find:
di = -0.15 m
The negative sign indicates that the image formed is virtual.
Step 2: Calculate the magnification (m) using the magnification formula.
Substituting the values into the magnification formula:
m = -di/do = -(-0.15)/0.6
m = 0.25
The positive magnification indicates that the image is upright.
Therefore, the image is located 0.15 m behind the mirror (since di is negative) and the magnification of the image is 0.25.