A convex mirror has a focal length of
-18 cm. How far behind the mirror does the image of a person 3.0 m away appear? The answer must be in cm.
The equation to use woulde be:
1/f = 1/do + 1/di
do = 300 cm
f = would it be -18 cm or 18 cm???
Use negatve numbers for the focal length of a convex mirror. They already tell you to use -18.
-1/18 = 1/300 + 1/di
1/di = -.058888
di = -16.98
Negative numbers for the di mean that the image is behind the mirror. This would be typical of a mirror used as a wide-angle side view mirror for a car, or for viewing aorund a corner.
In this case, the focal length of the convex mirror is given as -18 cm. The negative sign indicates that the mirror is a convex mirror. Convex mirrors always have negative focal lengths.
So, f = -18 cm.
Given:
do = 300 cm (distance of the person from the convex mirror)
Now, we can use the lens/mirror equation:
1/f = 1/do + 1/di
Substituting the values, we have:
1/-18 = 1/300 + 1/di
Now, let's solve for di (distance of the image behind the mirror):
1/di = 1/-18 - 1/300
To simplify, we find a common denominator:
1/di = (300 - 18)/(-18 * 300)
1/di = 282/(-18 * 300)
1/di = -282/5400
Now, we can obtain the value of di:
di = 5400/-282
di ≈ -19.15 cm (rounded to two decimal places)
Therefore, the image of the person appears approximately 19.15 cm behind the convex mirror.