A personal-grooming company wants to engineer a circular concave makeup mirror that produces an upright virtual image that is exactly twice the linear size of the user’s face when the face is 30 cm from the mirror surface.
Part (a)
Calculate the required distance between the image and the mirror.
Part (b)
Determine the focal length the mirror must have to meet the design specification.
Part (c)
Compute the radius of curvature of the mirror’s surface.
Part (d)
If the user unintentionally moves 5 cm closer to the mirror while applying makeup, determine the new linear magnification and state whether the image remains upright. Show all reasoning.
(1) Part (a) Calculate the required distance between the image and the mirror.
(2) Part (b) Determine the focal length the mirror must have to meet the design specification.
(3) Part (c) Compute the radius of curvature of the mirror’s surface.
(4) Part (d) If the user unintentionally moves 5 cm closer to the mirror while applying makeup, determine the new linear magnification and state whether the image remains upright. Show all reasoning.