A convex mirror has a focal length of 15 cm. A 3.0 cm high object is located 10 cm in front of this mirror. Where is the image located?
To answer this question, we can use the mirror formula, which is given by:
1/f = 1/d_o + 1/d_i
where:
- f is the focal length of the mirror,
- d_o is the object distance (distance between the object and the mirror), and
- d_i is the image distance (distance between the image and the mirror).
Given:
- f = 15 cm (focal length),
- d_o = -10 cm (negative sign denotes that the object is located in front of the mirror), and
- d_i = ? (to be determined).
Now, we can plug in these values into the mirror formula and solve for d_i.
1/15 = 1/-10 + 1/d_i
1/15 = -1/10 + 1/d_i
To simplify the equation, we multiply both sides by 150d_i:
10d_i = -15(150) + 150d_i
Now, we can solve for d_i:
10d_i - 150d_i = -15(150)
-140d_i = -15(150)
Dividing both sides by -140 gives:
d_i = (-15 * 150) / -140
d_i = 2250 / 140
d_i ≈ 16.07 cm
Therefore, the image is located approximately 16.07 cm behind the convex mirror.