An optical engineer wishes to specify the properties of a concave makeup mirror, which is supposed to provide an upright and enlarged image of the user's face. the engineer wants a magnification factor of two, and she assumes that the user's face will be 30 cm in front of the mirror. what radius of curvature should be specified (in cm) for the fabrication of these mirrors?

radius of curvature is 1.2 m

Explanation:

given data

distance u = 30 cm

to find out

radius of curvature

solution

we know radius of curvature is double of focal length

so we find focal length

lens formula for focal length

1/f = 1/u + 1/v     1

so here from magnification

M = - u /v

2 = - u /v )

v = -2u = -2(30)

v =- 60 cm

so from equation 1

1/f = 1/u + 1/v

1/f = 1/30 + 1/-60

f = 60.02 cm

so R = 2f

R = 2( 60.02)

R = 120.04 cm

so radius of curvature is 1.2 m