A concave spherical mirror has a radius of curvature of 50 cm.The image of an object located 35 cm in front of the mirror is
A)real,inverted,magnified 2.5 times,and 87.5 cm from the mirror.
B)real,erect,magnified 2.5 times,and 87.5 cm from the mirror.
C)virtual,erect,magnified 3.3 times,and 117 cm from the mirror.
D)real,inverted,magnified 3.3 times,and 117 cm from the mirror.
E)real,inverted,diminished 0.42 times,and 14.6 cm from the mirror.

Question

Quizplus · Accepted Answer

For a concave mirror, the mirror equation is $ \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. Given the radius of curvature is 50 cm, the focal length $f = \frac{R}{2} = 25$ cm. The object distance $u = -35$ cm (negative because it's in front of the mirror). Plugging these values into the mirror equation gives $ \frac{1}{25} = \frac{1}{v} - \frac{1}{35} $, solving for $v$ gives $v = 87.5$ cm, indicating the image is real and on the same side as the object (since $v$ is positive). The magnification $m = -\frac{v}{u} = -\frac{87.5}{-35} = 2.5$, indicating the image is inverted (since magnification is positive) and magnified 2.5 times.

A Concave Spherical Mirror Has a Radius of Curvature of 50