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.
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.