00:01
Hi there, so for this problem, we are told that the right side rear view mirror of mike's car says that the object in the mirror are closer than they appear.
00:11
Now, mike decides to do an experiment to determine the focal length of the mirror.
00:16
Now, he holds a plain mirror next to a rear view mirror and builds an object that is 160 centimeters away from each meter.
00:26
So the object distance is the same for both mirror.
00:30
And that is equal to 160 centimeters.
00:36
Now, the object appears 3 .16 centimeters wide in the plane mirror.
00:44
So the image hide for the plane mirror, so let's call this h .p .m.
00:58
By plain mirror is equal to 3 .6.
01:04
Centimeters.
01:06
Now, but only 1 .76 centimeters wide in the rear view.
01:12
So the height in the rear view is equal to 1 .76 centimeters.
01:27
So the question is, what is the focal length of the rear view mirror? now, with that said, we know that for a plain mirror, the focal length for a plane mirror, it just tends to infinity.
01:54
So if we use the thin length equation that we know is that the focal, the inverse of the focal lens is equal to the inverse of the object distance plus the inverse of the image distance.
02:05
So if the focal length tends to infinity, we can set this equal to zero.
02:11
And from this, we will obtain that the object distance is just simply equal to minus the image distance.
02:20
Now, once we know this, we can use the equation for the magnification, because we know that the magnification is the height of the image.
02:30
Well, in this case, let's call this the height of the image in the plane mirror divided by the initial height, the height of the object.
02:40
And then this is equal to minus the image distance divided by the object distance.
02:45
But we know that they are the same by assigning here.
02:49
So that will be just simply equals to 1.
02:52
So from here we can obtain that the image hide in a plain mirror is equal to just simply the height of the object.
03:03
So with that said, we know that the height of the object that we are looking with these two mirrors is just the height that we see in the plain mirror.
03:14
So that will be 3 .16 centimeters...