The image of a plant is 4.0 cm from a concave spherical mirror having a radius of curvature of 10 cm.Where is the plant relative to the mirror?
A) 2.2 cm in front of the mirror
B) 4.4 cm in front of the mirror
C) 9.0 cm in front of the mirror
D) 1.0 cm in front of the mirror
E) 20 cm in front of the mirror

Question

Quizplus · Accepted Answer

The mirror equation, $ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} $, where $f$ is the focal length, $v$ is the image distance, and $u$ is the object distance, can be used here. The focal length $f = \frac{R}{2} = 5 $ cm (since the radius of curvature $R = 10$ cm). Given $v = -4.0$ cm (negative because the image formed by concave mirrors is on the same side as the object), we can solve for $u$. Substituting the values, we get $ \frac{1}{5} = \frac{1}{-4} + \frac{1}{u} $, solving for $u$ gives $u \approx -2.2$ cm, indicating the object is 2.2 cm in front of the mirror (negative sign indicates the object is in front of the mirror).

The Image of a Plant Is 4