Answer to Question #299732 in Physics for miyay

Question

An object is placed in front of a convex mirror, and the size of the image is one-fourth that of the object. What is the ratio do/f of the object distance to the focal length of the mirror?

A.+3

B.-3

C.-2

D.+2

Answer 1

Given:

$m_i=\frac{1}{4}m_o$

The convex mirror equation says

$$\frac{1}{f}=\frac{1}{o}+\frac{1}{i}$$

The magnification

$$m_i/m_o=-i/o=1/4$$

Hence

$$i=-1/4o$$

Finally

$$\frac{1}{f}=\frac{1}{o}+\frac{1}{-1/4o}=\frac{-3}{o}$$

$$\frac{o}{f}=-3$$

Answer: B.-3