A makeup artist uses a concave mirror with a focal length of 12 cm to apply makeup with precision. If the client's face is positioned 24 cm from the mirror, how far is the image of the face located from the mirror's surface?-8 cm-24 cm+8 cm+24 cm
Question
A makeup artist uses a concave mirror with a focal length of 12 cm to apply makeup with precision. If the client's face is positioned 24 cm from the mirror, how far is the image of the face located from the mirror's surface?-8 cm-24 cm+8 cm+24 cm
Solution
To solve this problem, we can use the mirror formula, which is 1/f = 1/v + 1/u. Here, f is the focal length of the mirror, v is the image distance, and u is the object distance.
Given in the problem, f = -12 cm (it's negative because it's a concave mirror) and u = -24 cm (it's negative because the object is on the same side as the light being reflected).
Substituting these values into the mirror formula gives us:
1/-12 = 1/v - 1/-24
Solving this equation for v (the image distance) gives us v = -8 cm.
So, the image of the face is located 8 cm from the mirror's surface, on the same side as the face itself. Therefore, the correct answer is -8 cm.
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