A shaving/makeup mirror is designed to magnify your face by a factor of 1.33 when your face is placed 20.0 cm in front of it.
A) what type of mirror is it?
B)Describe the type of image that it makes of your face .
C) Calculate the required radius of curvature for the mirror.
A) To determine the type of mirror, we need to check whether the magnification factor is positive or negative. A positive magnification factor indicates a concave mirror, while a negative magnification factor indicates a convex mirror.
For this question, the magnification factor is 1.33, which is positive. Therefore, the mirror is a concave mirror.
B) The type of image formed by a concave mirror depends on the object's distance from the mirror's focal point.
1. If the object is placed beyond the focal point (F), the image will be real, inverted, and located between the focal point and the mirror.
2. If the object is placed at the focal point, the reflected rays will be parallel, and no image will be formed.
3. If the object is placed between the focal point and the mirror, the image will be virtual, upright, and magnified.
In this case, the object distance is 20.0 cm, which is less than the focal length (F). Therefore, the image formed will be virtual, upright, and magnified.
C) To calculate the required radius of curvature for the mirror, we can use the mirror formula:
1/f = 1/do + 1/di
Where f is the focal length, do is the object distance, and di is the image distance.
Since the image is virtual, the image distance (di) can be taken as negative.
Let's solve for the focal length (f) using the given information:
do = 20.0 cm
magnification factor (m) = 1.33
From the magnification factor, we can use the formula:
m = -di/do
Substituting the values:
1.33 = -di/20.0
Solving for di:
di = -26.6 cm
Now, substituting the values into the mirror formula:
1/f = 1/20.0 + 1/-26.6
Simplifying:
1/f = -0.05 + (-0.038)
1/f = -0.088
Solving for f:
f = -11.4 cm
The required radius of curvature for the mirror is equal to twice the focal length, so:
Radius of curvature = 2 * |-11.4 cm| = 22.8 cm
Therefore, the required radius of curvature for the mirror is 22.8 cm.