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) The type of mirror is a concave mirror. This is because a concave mirror has a converging effect, which means it can magnify objects when they are placed within its focal length.

B) The concave mirror will create a magnified, virtual image of your face. The image will be upright (not inverted) and larger in size compared to your actual face. Since the mirror is designed to magnify your face by a factor of 1.33, the image formed will be 1.33 times larger than the actual size of your face.

C) To calculate the required radius of curvature for the mirror, we need to use the mirror equation:

1/f = 1/di + 1/do

where:
- f is the focal length of the mirror,
- di is the image distance (which is negative for virtual images),
- do is the object distance (the distance between the object and the mirror).

In this case, the mirror magnifies the face by a factor of 1.33, which means the image distance (di) will be 1.33 times the object distance (do).

Given that the object distance (do) is 20.0 cm, and the magnification (m) is 1.33, we can substitute these values into the magnification equation:

m = -di/do

1.33 = -di/20.0

Solving for di, we get:

di = -20.0/1.33
di = -15.04 cm

Now, using the mirror equation, we can find the focal length (f) of the mirror:

1/f = 1/-15.04 + 1/20.0

Simplifying this equation, we get:

1/f = -0.0666 + 0.05

1/f = -0.0166

f = -1/0.0166
f ≈ -60.24 cm

The radius of curvature (R) of a concave mirror is twice the focal length:

R = 2f
R ≈ 2(-60.24) cm
R ≈ -120.48 cm

Therefore, the required radius of curvature for the mirror is approximately -120.48 cm (negative sign indicates that it is a concave mirror).