When you are very close to a particular makeup/shaving mirror, you notice that y
ID: 2244924 • Letter: W
Question
When you are very close to a particular makeup/shaving mirror, you notice that your reflection is upright and enlarged. Later, when you look at the mirror from various distances from far across the room, you find that your reflection is inverted, but not always enlarged.
a. The mirror is: (converging or diverging) and (concave/covex).
When your face is 10.0 cm away from your mirror, you find its image has a magnification +1.67.
b. What is the focal length of the mirror?
c. What is the radius of curvature of the mirror?
d. How far from the mirror should you put your face so that its image will have a magnification of -1.67?
Explanation / Answer
A. Since it is upright and enlarged, mirror is : converging, and convex
You are given do = 10cm, and M = +1.67
M = di/do, so di = 16.7cm
b. You can find focal length witht the equation
1/f = 1/di + 1/do
1/f = 1/10 + 1/16.7
f = 6.25cm
Radius of curvature = half focal length
R = 3.13cm
M = -1.67
di/do = -1.67, di = -1.67 do
1/f = 1/di + 1/do
1/6.25 = 1/-1.67do + 1/do
You can figure out the rest from here with simple algebra..
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