A shaving/makeup mirror is designed to magnify your face by a factor of 1.27 when your face is placed 23.5 cm in front of it. What type of mirror is it? Describe the type of image that it makes of your face. Calculate the required radius of curvature for the mirror.

Answer 1

The image distance must be -23.5 x 1.27 cm.

The minus sign means the image is behind the mirror. The image is virtual.
Image distance = di
Object distance = do
1/do + 1/di = 2/R

Now solve for R.

R, the radius of curvature, is a positive number. It is a concave mirror.

Answer 2

The mirror is concave (convex mirrors can only produce diminished images )
Image distance
1.27•23.5 =29.85 cm.
1/f = 1/di -1/do
1/f = 1/ 23.5 – 1/ 29.85 = 0.0091 cm
f = 109.9 =110cm = 1.1 m
R =2•1.1 = 2.2 m