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A woman's face is 20 cm in front of a concave makeup mirror having a focal length of magnitude 30 cm. How large is the image of her face?

A. four times as large as her face
B. of the same size as her face
C. twice as large as her face
D. three times as large as her face
E. half as large as her face

1 Answer

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Final answer:

The image of the woman's face formed by the concave makeup mirror is three times as large as her actual face.

Step-by-step explanation:

The image of the woman's face formed by the concave makeup mirror can be determined using the mirror formula: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. In this case, the object distance is 20 cm and the focal length is 30 cm. Plugging these values into the formula, we can solve for the image distance:

1/30 = 1/v - 1/20

5/600 = 1/v

v = 600/5 = 120 cm

Since the image distance is positive, the image is real. The magnification of the image is given by M = -v/u, where M is the magnification. Plugging in the values, we get:

M = -120/20 = -6

Therefore, the image of the woman's face is 6 times larger than her actual face. So, the correct answer is D. three times as large as her face.

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