# A lighted candle is 10 m away from a wall. A concave mirror is being used to project an image of the candle onto the wall. If the image is going to be 3.0 times the size of the object, how far should the mirror be from the wall?

We can use the magnification equation to help us out:

Magnification = the distance between the mirror and the image, divided by the distance between the object and the mirror.

In other words:

M = di / do

We’re trying to figure out how far the mirror should be from the image, so the variable we’re trying to solve for is di.

We already know the value of one variable: the image will be 3 times the size of the candle, so the magnification is 3.

[3] = di / do

Rearranging this problem so we can solve for di gives us:

di = (3)*(do)

di = 3do

If you look at the diagram below, you’ll see that the candle is 10m from the wall. do is the distance between the candle and the mirror, and di is the distance between the mirror and the wall. So in relation to each other:

do + 10m = di

di - do = 10m

Remember above when we solved for di? di = 3do. Let’s substitute that value in this equation:

3do - do = 10m

2do = 10m

do = 5m

Now let’s substitute the value of do in the equation di = 3do:

di = 3do

di = 3(5m)

di = 15m

This tells us that the distance between the image and the mirror is 15m. Therefore, the mirror should be placed 15m away from the wall.

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