A candle is 32.0 cm in front of a convex spherical mirror of radius of curvature 68.0 cm.What are the image distance and the magnification,respectively?
A)-16.5 cm,+ 0.515
B)-21.8 cm,- 1.94
C)-36.0 cm,+ 0.242
D)-1.9 cm,+ 1.94
E)16.5 cm,- 0.515

Question

Quizplus · Accepted Answer

The mirror equation is $ \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. For a convex mirror, $f$ is positive and equal to half the radius of curvature, so $f = \frac{68.0 \, \text{cm}}{2} = 34.0 \, \text{cm}$. Given $d_o = -32.0 \, \text{cm}$ (negative because the object is in front of the mirror), we can solve for $d_i$. Substituting the values, we get $ \frac{1}{34.0} = \frac{1}{-32.0} + \frac{1}{d_i} $, solving for $d_i$ gives $d_i = -16.5 \, \text{cm}$. The magnification $m = \frac{d_i}{d_o} = \frac{-16.5}{-32.0} = +0.515$.

A Candle Is 32