An object is held at a distance of 19.0 cm from a convex mirror creating an image that is 1/6 the object size.What is the focal length of the mirror?
A)-3.8 cm
B)16 cm
C)-2.7 cm
D)-8.8 cm
E)23 cm

Question

Quizplus · Accepted Answer

The magnification (m) is given by the ratio of the image distance (v) to the object distance (u), m = v/u. Since the image is 1/6 the size of the object, m = 1/6. Given that the object distance (u) is -19.0 cm (negative because it's on the same side of the mirror as the light source), we can find v = m*u = (1/6)*(-19.0 cm) = -3.17 cm. Using the mirror equation 1/f = 1/v + 1/u, where f is the focal length, we substitute v = -3.17 cm and u = -19.0 cm to solve for f. This gives 1/f = 1/(-3.17 cm) + 1/(-19.0 cm), which simplifies to f ≈ -3.8 cm.

An Object Is Held at a Distance of 19