Question

an object is placed 30.0 cm in front of a mirror. if it produces an image 50.0 cm away from the mirror and on the same side as the object, what is the radius of curvature of the mirror?+37.5 cm-37.5 cm-18.8 cmnone of the choices are correct.+18.8 cm

Explanation:

Step1: Determine sign conventions

For a mirror, object distance \(u = - 30.0\space cm\) (negative as per sign convention, object is in front of the mirror) and image distance \(v=-50.0\space cm\) (image on the same side as the object, so negative).

Step2: Use mirror formula

The mirror formula is \(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\).
Substitute \(u = - 30\) and \(v=-50\) into the formula:

$$
LATEXBLOCK0
$$

Step3: Relate focal length and radius of curvature

The relation between radius of curvature \(R\) and focal length \(f\) is \(R = 2f\).
Substitute \(f=-18.75\space cm\) into the formula: \(R=2\times(- 18.75)=-37.5\space cm\)

Answer:

-37.5 cm