Answer:
A) To calculate the image distance, we can use the mirror formula:
1/f = 1/di + 1/do
Where:
f = focal length of the mirror
di = image distance
do = object distance
Given that the focal length of the mirror is 50 cm and the magnification of the mirror is 0.10, we can find the image distance.
Using the magnification formula:
m = -di/do
Where:
m = magnification
di = image distance
do = object distance
We can substitute the given magnification value into the formula:
0.10 = -di/do
Rearranging the formula, we get:
do = -di/0.10
Now we can substitute the value of the focal length into the mirror formula:
1/50 = 1/di + 1/do
Simplifying the equation, we have:
1/di + 1/do = 1/50
Substituting the value of do from the magnification formula into the mirror formula, we get:
1/di + 1/(-di/0.10) = 1/50
Simplifying further, we have:
1/di - 10/di = 1/50
Combining the terms with a common denominator, we get:
-9/di = 1/50
Cross-multiplying, we have:
-9 * 50 = di
Therefore, the image distance is:
di = -450 cm (or -4.5 meters)
B) To calculate the object distance, we can use the magnification formula:
m = -di/do
Given that the magnification is 0.10, we can substitute the value of di (which we calculated earlier) into the formula:
0.10 = -(-450)/do
Simplifying the equation, we have:
0.10 = 450/do
Cross-multiplying, we get:
0.10 * do = 450
Therefore, the object distance is:
do = 4500 cm (or 45 meters)