Final answer:
Using the mirror equation and magnification formula, the object's distance do from a concave mirror with r = 11 cm and m = 2.6 is calculated to be 8.8 cm.
Step-by-step explanation:
To calculate the object's distance from a concave mirror when the radius of curvature (r) is given and the image magnification (m) is known, we can use the mirror equation and magnification formula. The mirror equation is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance from the mirror.
The magnification is given by m = -di/do. Since the magnification is positive, we have an upright image and the value of di has to be negative because concave mirrors produce virtual images when the object is inside the focal length.
First, we find the focal length f using the relation that f = r/2. For a radius of curvature of 11 cm, the focal length f of the concave mirror is 11/2 = 5.5 cm. Using the magnification formula m = -di/do and knowing m = 2.6, we rearrange to find -di = do × m. Substituting into the mirror equation, we now have 1/f = 1/do + 1/(-do × m).
Plugging the values we have into the equation, we get:
1/5.5 = 1/do - 1/(2.6 × do)
This simplifies to:
2.6/do - 1/do = 1/5.5
1.6/do = 1/5.5
do = 1.6 × 5.5
After calculating, we find the object distance do to be:
do = 8.8 cm.
Therefore, the object is placed 8.8 cm in front of the concave mirror.