You stand 5.2 meters away from a spherical mirror and your image forms 6.3 meters away on the front side of the mirror. What is your magnification?
To calculate the magnification of your image in this scenario, we need to use the mirror equation:
1/f = 1/di + 1/do
Where:
- f is the focal length of the mirror,
- di is the distance of the image from the mirror, and
- do is the distance of the object from the mirror.
Given that the image forms 6.3 meters away and the distance to the mirror is 5.2 meters, we can substitute these values into the equation:
1/f = 1/6.3 + 1/5.2
Now, to solve for f, we need to rearrange the equation:
1/f - 1/6.3 = 1/5.2
To combine the fractions:
(5.2 - 6.3)/f = 1/5.2
Now, let's solve for f:
f = (5.2 * 6.3) / (6.3 - 5.2)
f = 32.76 / 1.1
f ≈ 29.78 meters
Now that we know the focal length, we can calculate the magnification using the formula:
magnification (m) = -di / do
Given that the distance to the mirror (do) is 5.2 meters and the image distance (di) is 6.3 meters:
m = -6.3 / 5.2
m ≈ -1.21
Therefore, your magnification (m) is approximately -1.21. The negative sign indicates that the image is inverted compared to the object.