Answer to Question #2736 in Optics for rene

Question

You look into a shaving mirror and the upright image of your face is 40.0 cm away from you. The image has a magnification of 1.50. (a) How far away are you from the mirror? (b) What is the radius of curvature? all answers should be in cm. thanks.

Answer 1

For a concave mirror:
object distance from mirror = u (Object is your face)
Image distance from mirror = v

(a)& The image appears behind the mirror, and your face is in front, so the
distance from your face to the image is u + v

So u + v = 40
also magnification = v/u so v/u = 1.5

Therefore v = 1.5u and u + v = 40

Combining these two:-
u + 1.5u = 40
2.5u = 40

Your distance from mirror& u = 40/2.5 = 16cm.

also v = 1.5u
so v = 1.5 * 16 = 24cm.

(b)
The equation to find the focal length "f" is

1/u + 1/v = 1/f
so 1/f = 1/16 + 1/24

1/f = 3/48 + 2/48 = 5/48
so 1/f = 5/48

& Hence f = 48/5 = 9.6cm.
The radius of curvature of a concave mirror is twice the focal length f, so:
R = 2 * 9.6 = 19.2cm.