# Convex Mirrors Problem

## Homework Statement

A convex mirror of focal length 10cm forms an image that is one quarter the size of the object. Find the position of the object and the image.

-1/f = 1/u + 1/v
m = v/u

## The Attempt at a Solution

m = 1/4
f = 10cm
-1/10 = 1/u + 1/0.25u

I think that 1/u + 0.25u is the problem because I cant find the common denominator. The answer to the question is u = 30cm, v = 7.5cm just in case someone thinks I want them to do my homework for me. I just want to understand how to get it. Thanks.

CompuChip
Homework Helper
Dude, relax. Getting impatient after just one hour is not going to help you.
By the way, how does telling us that you know the answer prove anything?

Anyway, your last equation looks correct, except that you need to be careful with the sign of v... the mirror is convex, so it's like a negative lens: it will produce an image on the same side as the object. Hence, v = -0.25u.

Correcting that, you just have a problem with your math. Because in principle,
-1/10 = 1/u - 1/0.25u
is a single equation in one unknown (u), so you can easily solve for u.

Hint: multiply through by u.

I still don't understand. The point I'm trying to make is that I don't know how to get the common denominator when theres a fraction and a number. I just need someone to tell me how.

CompuChip
$$\frac{1}{u} = \frac{?}{0.25 \cdot u}$$