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An object and an observer are located $2 \mathrm{m}$ in front of a plane mirror, as shown in the following figure. If the observer is 3 m from the object, find the distance between the observer and the location of the object's image.

(Check your book to see image)

$5 \mathrm{m}$

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McMaster University

we have an observer located at point A that is three meters away from the object located at 30.0, both the observer and the object of the same distance away from a mirror which is the blue line. And this is two meters and it wants to know the distance to the image of the object to the observer. Okay, so basically, using the fact that objects image it in a flat plane mirror is the same distance appears to be the same distance on the other side of the mirror. So we're going to go to more meters in this direction to get to our image of the object here, we can call this point be so now to figure out the and this is also two meters away using this, using, um, the information about flat plain Mears. So now the question is to find the high pot news of what appears to be a right triangle, and it is a right triangle so we can just find the hype oddness of this right triangle. Or, in other words, since the ray let's think about it like this, the rays will draw in green are going to leave and then bounce back at the same angle they left to the observer here. So that means following the started line, the Observer would appear to see the image at this point be right. So that's why we need to find the pot on your side. So what we're gonna do is we're gonna use the fact that ah, right triangle a squared plus B squared is equal to C squared or, in other words, the total distance which we can call D. This distance here is equal to the square root as, uh, the distance between A and O squared, which is three meters squared, plus the distance between O and B, which is a total of four meters squared. So we have three squared plus four squared, all square rooted. Um, this is the square root of 25 or in other words, five meters. So we come box five meters in as the solution to our question