When a woman stands with her face 40.0 cm from a cosmetic mirror, the upright image is twice as tall as her fa

When a woman stands with her face 40.0 cm from a cosmetic mirror, the upright image is twice as tall as her face. What is the focal length of the mirror?When a woman stands with her face 40.0 cm from a cosmetic mirror, the upright image is twice as tall as her fa
M (magnification) = [Image height / Object height] = [Image distance / Object distance]


2 = x / 40


So image distance is 80cm


1/f = 1/u + 1/v


1/f = 1/40 + 1/80


1/f = 3/80


f = 30/3 cm


the focal length of the mirror is 10 cmWhen a woman stands with her face 40.0 cm from a cosmetic mirror, the upright image is twice as tall as her fa
M = -i/o, where M is the magnification, i is the image distance and o is the object distance. Since the image is upright, M is positive.





2 = -i/40 cm


i = -80 cm





Using the mirror formula, we have





1/f = 1/i + 1/o, where f is the focal length of the mirror.


1/f = 1/(-80) + 1/40


1/f = 1/80


f = 80 cm





The focal length is 80 cm.





The f we obtained is positive, thus the mirror used is a concave mirror. Upright (virtual) images are produced by a concave when the object is placed at a point closer than the mirror's focal length. They also become enlarged then.





Hope that helps.
there is alot of conditions effect the focal lenght like if the woman stand on the focal or not

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