Answer :
Final answer:
The object distance is 61.5 cm and the image distance is 39.1 cm.
Explanation:
To solve this problem, we can use the lens/mirror equation. Given that the focal length of the concave mirror is 22.7 cm and the distance between the object and the image is 39.1 cm, we can find the object distance and the image distance. The lens/mirror equation is:
1/do + 1/di = 1/f
where do is the object distance, di is the image distance, and f is the focal length. Rearranging the equation, we can solve for do:
do = 1 / (1/f - 1/di)
Substituting the given values, we have:
do = 1 / (1/22.7 - 1/39.1) = 61.5 cm
To find the image distance, we can use the formula:
di = do * (1 - f/do)
Substituting the given values, we have:
di = 61.5 * (1 - 22.7/61.5) = 39.1 cm
istances for a concave mirror can be calculated using the mirror formula. First, the image distance is calculated, which is then used to calculate the object distance.
In this problem, we are asked to find both the object distance and the image distance for a concave mirror. The provided key details are a focal length of 22.7 cm and a total distance between the object and its image is 39.1 cm. We can use the mirror formula, which is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.
In solving for (a) the object distance, we can first solve for the image distance by rearranging the equation to di = 1/(1/f - 1/do). Considering that the total distance (do+di) is given as 39.1cm, we end up with our calculation being di = 39.1cm - do. After finding di, we then plug this value into our original formula to solve for do. Similarly, for (b) the image distance, we take our previously calculated do value, and substitute it into the mirror formula solving for di.
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