A single convex spherical mirror is used to create an image of a 10.0-cm tall source that is located 35.0 cm to the left of the mirror.The magnitude of the radius of curvature for the mirror is 15.0 cm.Where does the image form?

Question

Quizplus · Accepted Answer

For a convex mirror, the image is always virtual, upright, and reduced in size, which means it forms on the same side as the object (to the right of the mirror in this context). The mirror equation, $ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} $, where $f$ is the focal length, $d_o$ is the object distance, and $d_i$ is the image distance, can be used to find the image location. The focal length $f$ of a convex mirror is positive and equal to half the radius of curvature, so $f = \frac{R}{2} = 7.5$ cm. Substituting $d_o = -35.0$ cm (negative because the object is in front of the mirror) and $f = 7.5$ cm into the mirror equation gives the image distance $d_i$, which calculates to approximately 6.2 cm to the right of the mirror.

A Single Convex Spherical Mirror Is Used to Create an Image