Answer to Question #122572 in Optics for Lisa

Question

2. A diverging mirror with a focal length of 25 cm has a magnification of 0.50. How far
apart are the object and the image?

Answer 1

Since, the lens is diverging ,thus $f$ is negative and $f=-25cm$

Formula for magnification is,

$$m=\frac{v}{u}$$

where, $u,v$ are object and image distance respectively.

Thus, $u=2v$

Now, from lens maker formula,

$$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$$

Hence,

$$\frac{1}{-25}=\frac{1}{v}-\frac{1}{2v}=\frac{1}{2v}\\ \implies v=-12.5cm$$

Thus,

$$u=-25cm$$