A retail chain installs spherical convex security mirrors near the ceiling so that employees standing at point S can monitor shoppers 5.0 m away along the main aisle. Management specifies that the virtual image of a shopper at that distance must appear no more than 1.5 m behind the mirror and be reduced to 0.30 times the shopper’s actual height.
Part (a)
Using the stated design goals, calculate the focal length that the convex mirror must have.
Part (b)
Determine the radius of curvature of the mirror’s surface.
Part (c)
Explain why a concave mirror would be unsuitable for meeting the same monitoring goals in this installation.
Part (d)
If the mirror is inadvertently manufactured with twice the required radius of curvature, quantify how the location and size of the shopper’s image would change for objects 5.0 m from the mirror. Support your answer with calculations.
(1) Part (a) Using the stated design goals, calculate the focal length that the convex mirror must have.
(2) Part (b) Determine the radius of curvature of the mirror’s surface.
(3) Part (c) Explain why a concave mirror would be unsuitable for meeting the same monitoring goals in this installation.
(4) Part (d) If the mirror is inadvertently manufactured with twice the required radius of curvature, quantify how the location and size of the shopper’s image would change for objects 5.0 m from the mirror. Support your answer with calculations.