Answer:
17 1/7 cm ≈ 17.1 cm in front of the mirror
Step-by-step explanation:
You want the location of the image formed of an object placed 40.0 cm in front of a concave mirror with radius of curvature 24.0 cm. The object is 2.5 cm tall.
a) Image location
For a spherical concave mirror with radius of curvature r, the relationship between the distance from the mirror to the image (i) and the distance from the mirror to the object (o) is ...
2/r = 1/i +1/o
Solving for i, we get ...
i = 1/(2/r -1/o) = 1/(2/24 -1/40) = 120/7 = 17 1/7 ≈ 17.1 . . . . cm
The image will be formed about 17.1 cm in front of the mirror.
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Additional comment
The magnification is -i/o = (-120/7)/40 = -3/7. The image height is about -15/14 ≈ -1.07 cm. The minus sign means the image is inverted with respect to the object.
The actual formula uses 1/f where f is the focal length. The "small angle approximation" for a spherical mirror says f = r/2, so 1/f = 2/r.
The attachment shows calculation of the image height as well as its location.
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