00:01
So we have an object of 2 centimeters high in front of a convex mirror with a focal length of 10 centimeters.
00:10
And we want to find the location of the image, the magnification of the image, and the orientation of the image.
00:17
The first thing you want to do for these optics problems is to draw out your ray diagram, identify the components, and orient yourself as to where these components are.
00:28
So for our first step we've drawn out this diagram.
00:34
We have our object here, which is located to our left.
00:37
We have our mirror, which is located right here.
00:40
And for this kind of problem, we see that we have two rays.
00:45
Once you have our object in our mirror, you want to draw one ray of light that is parallel to our principal axis, which you see which is down here.
00:55
This ray of light is parallel to our principal axis, and then it hits our mirror and then it deflects or diverges.
01:04
And for this mirror, since it's a convex mirror, you want to have a virtual ray of light that connects to the real deflection, the real deflection of this light.
01:18
And that's our going to be our first ray, so i'll just label this as ray number one.
01:27
Yeah, just label this number one.
01:39
For our second ray, we have to have at least two ways to determine our image.
01:44
The second rays, one that goes toward the focal point of our mirror.
01:50
And since this is a convex mirror, the focal point is going to be behind the mirror.
01:57
So our second ray of light goes toward a mirror, and then it reflects from this mirror and turns out parallel to the principal axis.
02:06
So it's the opposite of our first ray of light, which was incident parallel to our principal axis.
02:13
And then turned out or deflected.
02:17
And this deflection for ray 1 actually intersects with our focal point when it comes to our virtual part of this ray.
02:27
So i'll label our second ray number two.
02:33
So we have our object here, make sure i have a label that, we have our convex mirror, we have our two rays of light.
02:41
And from these rays of light you can see that there's virtual rays that intersect at this point, in order to connect the real rays that form when they deflect off of the mirror.
02:55
So at this point of intersection we have our image, that's where our image forms, and right next to it is our focal point.
03:06
So that's the point that is intersected by our first ray, and that's also by our second ray, but it deflects to the mirror first and turns out parallel.
03:21
So now that we have everything labeled, labeled, we need to orient ourselves.
03:25
So with all these problems, we always know that our mirror will be placed at zero for our number line.
03:34
And then anything that's labeled to the left of it will be a positive length.
03:39
And anything to the right will be labeled as a negative length.
03:43
So any object length or image length or focal length to the left or in front of the mirror, it's going to be positive.
03:52
And then anything behind it is going to be a negative length.
03:57
So since we have all this in mind, we can start using what we have given to us to solve this problem.
04:07
So we're given our focal length, and since our focal length is behind the convex mirror, that's usually the case when we have our convex mirror drawn like this.
04:20
Our focal length is going to be to the right of the convex mirror.
04:24
And anything to the right of the mirror, going to be negative.
04:27
So our focal length is going to be minus 10 centimeters...